and Windows 7!

I’ve been thinking recently of how to help investors get started when they have a month-to-month surplus but haven’t yet accumulated a pile of cash to buy a property, business, or other investment. The simplest way to handle it, of course, would be to just borrow money from a new investor at a rate that would leave them with a reasonably-sized pile at the end.

To make sure the lender is protected, I’d probably secure the loan against a piece of real estate or something else of value.

If I were to borrow $900 per month from an investor for 10 years, at 8% yield, how much would I owe them at the end of the 10 years?

This one is a pretty straightforward time-value-of-money (TVM) calculation.

First things first, make sure the calculator is using 12 Payments per Year.

N: 120 (I’m borrowing monthly for 10 years)

I/YR: 8 (I’m borrowing at 8% interest)

PV: 0 (They don’t start with any money)

PMT: 900 (I borrow $900 per month)

FV: (this is what I’m trying to find)

At the end of the 10 years, I’d owe my lender **$164,651.43**.

There are upsides and downsides to borrowing money with these kinds of terms, both for me and for the lender. I’ve been considering other ways of structuring such deals, and if you’re interested in those, come back in future weeks, as I’ll probably write about at least 2 or 3 more soon.

What do you think? Would you want to lend money like this? How about being on the borrowing side? Let us know in the comments below!

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**THE SCENARIO**

This Money Blog is a little different than some of the others and covers a couple of things which may be new to you. It’s okay, don’t freak out, I’ll try to explain everything in detail. However, I’m going to abbreviate some of the details to simplify the problem and make the concepts easier to grasp.

I’ve got a friend (call her Jill) who has a HELOC (a Home Equity Line Of Credit) that’s about to have its payment go up quite dramatically, and this will cause her some month-to-month cash flow issues for the next 10 years. I’ve got another friend (call him Tom) who wants to start investing, but doesn’t have a pile of cash to plunk down. He does, however, make more money per month than he spends, and he’d like to invest the difference.

Jill’s HELOC payment is about to go up by about $750 per month, and Tom’s got $750 per month to invest.

Before we go any further, let’s cover a bit of terminology. An ‘option’ is the *right to purchase* a ‘thing’ at some point in the future. When you ‘exercise’ the option, that means that you buy the ‘thing’. Much of the time, the ‘things’ covered by options are securities (i.e. stocks), houses, or other types of real estate, but technically an option could be sold against pretty much any ‘thing’.

Generally, options have several components:

- What you pay for the right to purchase (referred to as “Consideration”)
- A purchase price (or an agreement on how to determine the price at a later date)
- A time frame in which you can exercise the option (maybe I’ll have the right to purchase any time in the next 10 years)

For example, I could (a) pay you $10,000 now for the right to buy your house for (b) $500,000 between (c) 5 and 10 years from now. The Consideration is generally credited toward the purchase if the option is exercised (so in this example if I were to exercise my option, I’d only have to come up with $500,000 – $10,000 = $490,000 to actually do the purchase – I’ve already given you the first $10,000 when I bought the option in the first place).

If I don’t exercise the option within its time frame, it ‘expires’, meaning that it can no longer be executed. The consideration is not refunded in this case.

Okay, back to Tom helping Jill out with her cash flow shortfall.

Jill sells an option to purchase **20% ownership of the property** to Tom for $750 per month. Tom’s purchase price is $90,000 (which is $750 x 120), so his option consideration will completely cover his cost to exercise the option. This option will have no expiration, but will be exercised automatically if the property is sold. Tom and Jill will have to figure out what happens if the property is sold before the end of the 10th year, but that conversation is not part of this post.

**THE QUESTION**

If Jill sells the property at the end of the 10th year, how much would the property need to sell for in order for Tom to make 12% on his money? Assume that sales costs are 10% of the sale price (e.g. if you sell a house for $100,000, you walk away with 10% less, or $90,000).

**THE SOLUTION**

This seems more confusing than it actually is, but it does have a few parts.

First, we need to figure out how much value Tom would need to get from the property if he wanted to make 12% on his money.

Second, we need to figure out what the net proceeds of the sale of the property would have to be in order for Tom’s 20% share to hit that number.

Third, we need to figure out how much the property would have to sell for in order to net out that amount.

**Step 1**

Let’s restate the problem, from Tom’s perspective.

“If I invest $750 per month for 120 months and then receive a large cash payout, how large would the payout need to be in order for my investment to be worth at a 12% yield?” That’s a relatively straightforward Time-Value of Money problem.

First things first, make sure the calculator is using 12 Payments per Year.

N: 120 (Tom’s investing for 10 years, or 120 months)

I/YR: 12 (Tom wants to get a 12% yield on his money)

PV: 0

PMT: -750 (Tom’s investing $750 per month)

FV: (this is what I’m trying to find)

For Tom’s investment to yield 12%, his **20% of the property** would have to be worth **$172,528.02** after 10 years.

**Step 2**

If Tom’s portion of the proceeds of the sale is worth $172,528.02, the whole sale must net out $172,528.02 / 20% = **$862,645.09**.

**Step 3**

Since 10% of the purchase price will be eaten up by sales costs, we need to sell it for a little more than that. Jill would need to sell it for $862,645.09 / 90% = **$958,494.54** in order for Tom’s portion to be worth his target amount.

This one may have been a bit more confusing than some posts, largely because it combined the concepts of both an installment sale and an option. However, I’ve recently been considering the question of how people with smaller amounts of money to invest can get started investing, and this was one of the things I came up with.

What do you think? If you were Tom, would you make this investment? If you were Jill, would this sort of arrangement appeal to you? Let us know in the comments below!

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A friend of mine has a Home Equity Line of Credit (HELOC) that she got nearly 10 years ago. For those 10 years, the loan has been interest only, and the rate is Prime minus 1%.

Most HELOCs are ‘adjustable’, which means that their interest rate changes over time. Adjustable loans are generally tied to an ‘index’, such as Prime, COFI (Cost of Funds Index), or LIBOR (London Interbank Offered Rate), and generally have some spread, which is the amount above or below the index the charged rate will be. My friend’s loan is tied to Prime, and the spread is -1 percentage point. So if Prime is 4% in a given month, my friend’s loan will be at 3% interest for that month.

This HELOC is a bit different than other loans I’ve run across, in that after the 10-year interest-only period, it switches to a 10-year straight-line amortization. What that means is that when the interest-only period ends, the lender takes the amount still owed, divides it by the 120 months in the 10-year payoff period, and increases the payment for each of those months by the result. Each monthly payment still has an interest component, and that’s figured the same way it always has been: multiplying the monthly rate by the amount still owed when the month began.

Don’t worry, that’s less confusing than it sounds, and it’ll be clearer once we start seeing some actual numbers.

Okay, my friend currently owes $89,598.55, and her monthly (interest-only) payment is $245.96.

My questions is: If she came up with the money to pay off the loan up-front, what would her return on the $89,598.55 be?

For the purposes of this question, we’ll assume that the interest portion of each payment would be static at $245.96, even though in reality it would change each month as the principal gets paid off, and as the interest rate fluctuates over time.

This question is actually pretty straightforward, and it has 3 steps.

First, we have to find out how much principal will be required on each of the 120 payments.

Next, we have to find out what the principal + interest payment would be.

Last, we need to find the ROI on the $89k payment.

**Step 1**

The principal portion of each payment will be $89,598.55 / 120 = **$746.65**.

**Step 2**

The total monthly payment will be $746.65 + $245.96 = **$992.61**

**Step 3**

First things first, make sure the calculator is using 12 Payments per Year.

N: 120

I/YR: (this is what I’m trying to find)

PV: -89,598.55 (the amount my friend will have to pay to satisfy the loan)

PMT: 992.61 (the amount of each payment she won’t have to make)

FV: 0

The answer to the question is that my friend will get a **5.95%** return on her $89k if she pays off the loan immediately instead of making the monthly payments over the next 10 years.

What do you think? Would you pay off the loan on day 1? Or do you think you could do something with the $89k that would generate more money over time, thus potentially offsetting the now-larger monthly payments? Let us know in the comments!

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**THE SCENARIO**

A few years ago I bought a new car (well, it’s a used car, but it was new to me). The initial financing terms were not super-great, but the loan was easy to get as part of the purchase. Because I was confident in my ability to refinance after the fact, I took out that initial loan.

That original loan had 60 monthly payments of $236.

I then proceeded to shop around for a better car loan, and found one with a *much* better interest rate.

The loan I could refinance into had 60 monthly payments of $206.

Assuming I wanted to make 15% on my money, and assuming that I was able to refinance within the first month of the original loan (making the time period covered by the two loans the same), what’s the most I could pay to do the refinance?

**THE SOLUTION**

This one is fairly straightforward, but some readers may be thrown by the fact that I told you nearly nothing about the two loans in question. The good news is that to find the answer, you don’t have to know how much I borrowed (on either loan – the amounts might not be the same) *or* the interest rates on either loan. Why? The question is about the *differences* between the two loans, *not* about the loans themselves.

Since the second loan is $206 per month, and the original loan was $236 per month, if I do the refinance, I’m saving $236 – $206 = $30 per month over the life of the loan.

First things first, make sure the calculator is using 12 Payments per Year.

N: 60 (I’m saving money each month for 60 months)

I/YR: 15 (I want to make 15% on my refinancing costs)

PV: *(This is what I’m trying to find)*

PMT: 30 (I’m saving $30 per month over the life of the loan)

FV: 0 (When the loan is paid off, the savings ends… but at that point I won’t have a car payment anymore, so I’ll be even better off)

The answer to the question is the most I could pay to do the refinance would be **$1,261.04**.

I actually paid more for the refinance than the target amount ($1,261.04), but I was able to roll the costs into the refinanced balance, so I didn’t have to pay anything out-of-pocket. I was able to do this by dropping the interest rate enough that the savings *still* came out to $30 per month.

The only risk there was that my new balance might be more than the car was worth, but part of the refinance cost was the purchase of a ‘Gap Insurance’ policy, which covers the difference in case my car is totaled and my auto insurance pays out less than I owe on the loan.

What do you think? Would you do this kind of refinance? Could you do one right now?

Let us know in the comments!

and Windows 7!

**THE SCENARIO**

Generally, when you buy a house and get a mortgage but put less than 20% down, you have to pay for Private Mortgage Insurance, or PMI. PMI is an insurance policy that you pay for, but which insures the lender, in case you default on the loan. In most instances, you can get rid of your PMI policy when you have a certain amount of equity in the property, but the exact terms vary for each loan.

Several years ago, I got a loan and put less than 20% down, so for those several years, I’ve been paying $308.72 per month* for the PMI policy. I recently inquired about what I would have to do to make the PMI go away (I would prefer *not* to pay that money for someone else’s insurance policy), and I was told that I would have to pay down the loan to 78% of the original purchase price of the house. I bought the house for $390,000, and currently owe $332,057.02. The interest rate is 3.50%, and my payment is $1,680.35 per month (just on the loan, not including PMI, insurance, or taxes).

My question is: If I pay to remove the PMI, how much do I have to pay, and what’s my cash-on-cash return on that money?

* Note that each year, the PMI payment is recalculated, and it goes down by a few dollars for each of the next 12 months, due to the amortization that has occurred during that year. For the purposes of this question, though, I’m going to assume that the PMI payment stays the same, because that makes it simpler and it won’t change the end result very much (the year-over-year decreases tend to be in the realm of 1%).

**THE SOLUTION**

This problem has several steps.

First, I have to figure out how much 78% of the original purchase price of the house is.

Second, I have to figure out how much I’d have to pay today to get to that amount-owed.

Third, I have to figure out how long it would take me to reach that same point if I just continued to make my regular monthly payments.

Fourth, I need to find out what my return on the result from Step 2 is over the length of time I found in Step 3.

Let’s get to it.

**Step 1**

My original purchase price was $390,000, and 78% of that is

$390,000 x 0.78 = **$304,200**

**Step 2**

I currently owe $332,057.02, so if I wanted to pay down to $304,200, I’d have to pay

$332,057.02 – $304,200 = $27,857.02

I’d have to pay **$27,857.02** today to get my balance down to $304,200, at which point I’d owe 78% of the original purchase price.

**Step 3**

I need to find out how long it will take to reach $304,200 if I continued my regular monthly payments.

First things first, make sure the calculator is using 12 Payments per Year.

N: (this is what I’m trying to find)

I/YR: 3.50%

PV: 332,057.02

PMT: -1,680.35

FV: -304,200.00

I currently owe $332,057.02, so if I continue to make my normal $1,680.35 payment each month, it will take me **37.11 months** to pay the loan balance down to $304,200.

**Step 4**

I need to find out what the return on my $27,857.02 is when it saves me $308.72 per month for the next 38 months.

First things first, make sure the calculator is using 12 Payments per Year.

N: 38

I/YR: (this is what I’m trying to find)

PV: -27,857.02

PMT: 308.72

FV: 0

The answer to the question is that my cash-on-cash return on my **$27,857.02** payment today would be **-46.59%**. (Note, however, that due to paying off part of the debt, my long-term return would actually be positive – between 5.78% and 16.9%. If you’re interested in knowing more about this, leave a comment below and maybe I’ll cover it in a future post.)

I detest paying PMI. I mean, I really hate it. I consider PMI to be a bit of a racket, in fact, as you pay the premium to insure against your default, but your default is more likely because you’re paying hundreds of extra dollars per month that you could use to, you know, make sure that you can pay your mortgage. So I really *really* want to get rid of the PMI payment.

That being said, there’s no way I want to pay a sizable chunk of cash right now which yields almost -50%. If I wanted to get that kind of return on my money, I’d play the lottery. So for now, I think I’ll bide my time, wait another 3 years, and let amortization get me to my 78% target instead of making a 5-figure principal payment today.

What do you think? Would you do it? Let us know in the comments below!

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**THE SCENARIO**

Earlier this week, I went shopping at Costco, where I get a lot of my staple foods, paper products, cleaning supplies, gasoline, and other essentials. I knew that my “Gold Star” membership was expiring, and that I would have to pay $60 to renew it in order to buy the things I wanted to buy that day. When I went up to the Membership counter, I saw that they also have an Executive membership, which costs $120. What do you get for that extra $60? The main thing is that at the end of the year, they send you a rebate check amounting to 2% of your purchases over the year. There are other advertised benefits, but I don’t know that I’d be able to take advantage of any of them reliably, so I had to make my decision based entirely upon the rebate.

So the question is this: If I want to make 15% on my money, how much would I need to spend per month (on average) to justify getting the Executive membership instead of just renewing my Gold Star membership?

This problem has 3 steps. First, I need to find out how big the end-of-year rebate check should be to make me 15% on the extra $60 that the executive membership costs.

Then, I need to figure out how much I’d need to spend over the year to get a end-of-year rebate check of that amount.

Then, I need to figure out how much I’d need to spend each month (on average) to add up to that total annual amount.

Let’s get started.

**Step 1**

First things first, make sure the calculator is using 12 Payments per Year.

N: 12 (I get the rebate check after one year)

I/YR: 15 (I want to make 15% on my money)

PV: -60 (I have to pay an extra $60 to get the Executive membership)

PMT: 0 (I only get the rebate check at the end of the year; checks don’t arrive in the meantime)

FV: (this is what I’m trying to find)

The answer to Step 1 is that my rebate check would have to be at least **$69.65** for me to make 15% on my money. Note that due to monthly compounding, this number is slightly higher than 115% of $60.

**Step 2**

2% of [total annual spending] = $69.65

2% is another way of writing 0.02

Therefore, [total annual spending] = $69.65 / 0.02 = $3,482.26

The answer to Step 2 is that I’d have to spend at least **$3,482.26** over the next year to get a rebate check that large.

**Step 3**

If I spend $3,482.26 over a whole year, that means that I spend $3,482.26 / 12 each month (on average).

The answer to the whole question is that I’d have to spend an average of **$290.19** per month in order to get a rebate check big enough to get me 15% on the extra $60 I’d spent on the Executive membership.

I generally don’t spend $290.19 per month on staples at Costco, so upgrading to the Excecutive membership probably wouldn’t make sense for me *unless* I thought it likely that I’d be buying one or more big-ticket items there (like a computer, iPad, TV, etc.) in the next year. In that case, I’d adjust the amount I’d need to spend in the year based on that extraordinary planned purchase (for example, if I planned to buy $2,500 worth of iPads, computers, TVs, and other big-ticket items, my annual number would go from $3,482.26 to $982.26) and use $982.26 to determine my required average monthly spending to compare with my normal monthly spending. Obviously, I wouldn’t want to spend extra money just to get a 2% rebate, but if I’d already planned to do the spending, then setting up a rebate ahead of time might be a smart move. Does that make sense? Let us know what you think in the comments below!

and Windows 7!

**THE SCENARIO**

Several years ago, I moved from a medium-sized house with a garage to a small condo with no garage. As you might imagine, some of the ‘treasures’ I’d accumulated and stuffed into my house and garage just don’t fit into the much-smaller condo. So I did what so many of us do and rented a storage unit to keep the items I just couldn’t bear to part with (this was after seven van-loads of donations to the local Goodwill).

The storage center my extra stuff is currently housed in charges $176 per month for a 10’x10′ unit like mine (now I know what business I should *really* be in). However, if you pay for 6 months in advance, they’ll give you the sixth month for half off.

So my question is “if I pre-pay for six months, what’s the return on my up-front money?”

**THE SOLUTION**

It’s useful to re-state the problem to put it in terms that make it easier to plug into the calculator.

First off, I need to figure out how much money I have to pay up-front. Since they’re giving me Month 6 at half off, that means that I have to pay for 5 ½ months today to rent the unit for the next six months. Since once month costs $176, I have to pay $176 x 5.5 = $968 today.

So the restatement of the problem goes like this: I’m going to pay $968 now to save myself a $176 monthly payment for the next six months.

First things first, make sure the calculator is using 12 Payments per Year.

N: 6

I/YR: (this is what I’m trying to find)

PV: -968 (the amount I need to pay today…)

PMT: 176 (… to save this much each month)

FV: 0

The answer to the question is **30.53%**. So if I pre-pay for six months, I’m actually making over 30% on my money.

Making 30% on your money is something that, if you do it consistently and with enough money, can leave you pretty wealthy after a relatively short period of time. However, contrary to sales pitches in the vein of ‘The more you buy, the more you save!’, it usually doesn’t make sense to spend money just to get a *discount* on the price. If you can avoid the price (discounted or not), you’re generally better off. If I were to move into a bigger place or have a change of heart and decide to liquidate everything in the storage unit, I’d save myself $176 per month *without* the $968 payment every six months. And that would leave me nearly $2,000 per year richer than I am now.

What do you think? Do you have any pre-payment opportunities on your regular monthly payments, and if so, what’s the return on those up-front payments?

Let us know in the comments below!

and Windows 7!

**THE SCENARIO**

I’ve recently been talking with a lender to refinance a property. They told me that they can lend me $97,500 for 30 years at 7.375%, fully amortizing. They also said that if I paid them $2,015, they could reduce the rate to 6.5%. This is a commonly-available feature when you’re getting a new loan, and is called ‘buying down the rate’. Many times, the bank will have a variety of options with different costs, and they often won’t tell you about it unless you ask. But sometimes it can be worth it to do a rate buy-down.

So I’m considering whether to just take the ‘standard’ refinance rate, or whether to pay the money to get the lower rate.

My question is ‘If I buy down the rate, what’s my return on the $2,015 I have to spend in order to do so?’

**THE SOLUTION**

This is a four-parter, but each of the parts is fairly straightforward.

First, I need to find out how much I’d pay per month if I took the loan at the 7.375% rate.

Second, I need to find out how much I’d pay per month if I bought the rate down to 6.5%.

Third, I need to use these two numbers to figure out how much money I save each month if I buy down the rate.

Fourth, I need to find out what my return on my $2,015 up-front cost (to buy down the rate) is.

This may seem daunting, but if we take it one step at a time, we’ll see that there’s nothing tricky going on here.

Let’s get started.

First things first, make sure the calculator is using 12 Payments per Year.

**Step 1: The ‘normal’ loan**

N: 360

I/YR: 7.375

PV: 97,500

PMT: (this is what I’m trying to find)

FV: 0

Step 1 answer: **-673.41**. So if I took this loan, I’d pay $673.41 every month.

**Step 2: The ‘buy-down’ loan**

N: 360

I/YR: 6.5

PV: 97,500

PMT: (this is what I’m trying to find)

FV: 0

Step 2 answer: **-616.27**. So if I bought down the rate, I’d pay $616.27 every month.

**Step 3: What’s my monthly savings?**

If I pay $616.27 from the lower rate instead of $673.41 from the higher rate, I save $57.14 per month.

Step 3 answer: If I buy down the rate, I save **$57.14** each month.

**Step 4: The return on the buy-down cost**

N: 360

I/YR: (this is what I’m trying to find)

PV: -2,015 (if I pay this much today…)

PMT: 57.14 (… then I save this much each month)

FV: 0

The answer to the question is **34.03%**. So if I buy down the rate, I make a 34% return on the $2,015 I spend to do the buy-down.

As I mentioned at the top, when you go to get a loan, there are often a variety of different rates available to you, and those rates carry a variety of costs. Sometimes, you can take a *higher rate* and the bank will actually *give you money* to take the loan. It’s very important to be able to figure out which buy-down (or buy-up) option makes the most sense, and now that we’ve been through the process, you should be able to analyze your own loan prospects next time you’re talking to a bank. What do you think? Leave a comment below!

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**THE SCENARIO**

My friend recently had the chance to sell a house they own, and they had two offers from prospective buyers.

In both situations, sales costs and commissions will be 6% of the purchase price.

Option 1: The first buyer wants to buy the house for $75,000 cash. After sales costs, my friend would walk away with $70,500.

Option 2: The second buyer wants to buy the house for $85,000. They’d pay my friend $5,000 today, and $925 per month for the next 154 months. This sort of financing is made easier by hiring a servicer, which charges $25 per month for handling the paperwork. After sales costs, my friend would have to bring $100 to the table to close the deal (yes, they’d actually have to *pay* to sell their house). If you’re interested, check out this other Money Blog post that goes into this sort of sale in greater detail.

The question is: What is the return on my friend’s investment if they choose Option 2? Ignore the fact that taxes exist for the purposes of this exercise.

**THE SOLUTION**

First things first, make sure the calculator is using 12 Payments per Year.

Also, let’s rephrase the situation: my friend is going to give up $70,500 today *and also pay $100 today* in order to get $900 per month (the $925 payment minus the $25 servicing fee) for 154 months.

N: 154

I/YR: (this is what I’m trying to find)

PV: -70,600 ($70,500 that’s being given up, plus $100 that’s paid today)

PMT: 900 ($925 gross payment, minus the $25 that the servicer takes)

FV: 0

The answer to the question is that my friend will earn **11.99%** on the $70,600 they’re giving up today.

It’s tempting to take a pile of cash today instead of a stream of payments over time. In some cases, it’s the right answer, and in some cases taking the payments makes more sense. If my friend can easily earn more than 11.99% on their money, then taking the lump-sum payment (and then investing it at that higher rate) makes more sense than taking the payments over time. If, on the other hand, my friend would take the $70,600 and invest it at less than 11.99%, then taking the payments over time has the edge. What would you do in this situation? Leave a comment below and let us know!

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**THE SCENARIO**

I was talking with friends recently who are selling a house they own in another state. They had a couple of offers on the table, but were strongly leaning toward taking the one that involved taking payments over time instead of getting a huge pile of money on the close of escrow. (This is called ‘seller carry’, ‘selling on terms’, and ‘seller financing’, among other terms.)

The house is being sold for $85,000 with $5,000 down, and the balance is being financed at 10% for 154 months, at which point the buyer will own it outright. The question, then, is ‘How much money is the buyer going to give the seller every month for those 154 months?’

**THE SOLUTION**

First things first, make sure the calculator is using 12 Payments per Year.

N: 154

I/YR: 10

PV: -80,000 (this is negative because this is the amount of *value* the seller is giving the buyer in exchange for payments over time)

PMT: (this is what I’m trying to find)

FV: 0

The answer to the question is that the buyer will pay the seller **$924.12** per month until the house is paid off.

You may ask yourself ‘Why would the buyer want to do this? Current rates from a bank are in the neighborhood of 5%, so why would they want to accept 10% financing?’ Think about that question, and also think about why the seller would want to do this deal instead of just taking a pile of money today. Feel free to leave your ideas in the comments below!

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