and Windows 7!

**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!

and Windows 7!

**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!

]]>and Windows 7!

**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!

]]>and Windows 7!

**THE SCENARIO**

In 2016, I ran across a company called Arcadia Power* that lets you transition 50% or 100% of your electricity usage to wind power. Since the 50% option didn’t increase my bill at all, I decided to give it a shot, and it’s worked so well that everything has been the same on my end (except that their auto-pay was easier to set up than Southern California Edison’s had been).

Last week, they started up a new program where you can purchase solar cells located in various places around the US, and the electricity the cells generates defrays your own electricity expenses. It’s an interesting concept to a high-rise dweller like me, as I’d like to use solar power, but I don’t have a roof to put solar cells on. Even if I did have a roof, the program is interesting because the solar power would follow me even if I moved (it’s tied to my Arcadia account, not the physical location of my home, and my Arcadia account follows me wherever I move).

Looking into the page they set up about the program, the offer is as follows:

I’m interested in using renewable energy sources, and I’m interested in making money through investing, and this seems to be a way to do both at once… the question that remains, then, is ‘what’s the return on my investment if I buy one of these solar panels?’

* Full disclosure: This is a referral link, so if you sign up with Arcadia Power, you’ll get a billing credit and so will I. If you don’t like using referral links, feel free to use this link instead.

**THE SOLUTION**

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

Each solar cell I buy will look like this.

N: 120

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

PV: -300 (the cost of purchasing one panel)

PMT: 2.93 (the monthly energy savings from one panel)

FV: 0

If I buy solar cells, I get a **3.24%** return on my investment.

If a 3.24% return is good enough for me, or if the combination of 3.24% return and the environmental/societal benefits of supporting solar power over non-renewable energy sources is sufficiently compelling, this seems like an investment that could work well. I’d obviously need to read the fine print if I wanted to proceed, but if the numbers of an investment don’t work, there’s no reason to conduct the rest of the ‘due diligence’.

]]>and Windows 7!

**THE SCENARIO**

When people consider whether or not to pursue a new money-making venture, we often think of it in terms of ‘is giving this thing a shot worth it?’ This post takes a look at one example situation I found myself in recently and the thought process I used.

A few years back, I went to a meeting at an insurance agency with an emphasis on recruiting new insurance agents. There was a one-time up-front cost of $100 to get started with them, and then you’d go through training (call it $150), take your licensing exam and pay for your license (around $250 overall), and some immediate Continuing Education (CE) requirements that cost about $40. Once you got all that taken care of, you had to get an Errors and Omissions (E&O) insurance policy so that if you accidentally messed something up while selling a policy, you weren’t sent to the poor house. These policies cost about $35 per month at the time.

The license lasts for 2 years, and for the sake of this example, I’m going to completely leave out the value of my time and effort – the training alone is over 70 hours between pre-licensing and continuing education requirements, to say nothing of the time and effort spent to find a customer and sell them a policy.

For the sake of simplicity, I’m going to assume that I could do turbo-training and get all of my one-time up-front costs done right off the bat, so I’m going to lump those costs into a single ‘PV’ figure. I’m also going to assume that I will only sell one policy, all the way at the end of the two years over which the license is valid. The commission for this policy (i.e. what I’d be paid) would be $1,500 (this is a round number that’s in the range of commissions for people selling the types of policies that the company specializes in).

My question is, what is my return on investment (again: dollars only, leaving out the value of my time) if I sign up and everything works out as planned?

**THE SOLUTION**

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

N: 24

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

PV: -1 x (100 + 150 + 250 + 40) = -540

PMT: -35

FV: 1500

When I plug everything into the calculator, I learn that the return on my dollars invested is **6.06 %**.

If it were you, would you consider this a good thing to do? How many hours would you be willing to spend to make a return like this?

]]>and Windows 7!

**THE SCENARIO**

Several years ago I borrowed some money to buy a condo. Today, still owe $66,924.65 on this mortgage, with payments of $352.16 per month, at a rate of 3.875%.

If I suddenly came into a pile of money and decided to pay off this mortgage today, how much interest would I avoid paying over the remaining life of the mortgage by doing so?

For simplicity, assume that there’s no partial-month interest to satisfy and no pre-payment penalties involved.

**THE SOLUTION**

This problem is a three-stepper.

- The first thing we need to do is figure out how many payments are left on the mortgage.
- Then we need to figure out how much the total payments over that number of months would have been.
- Then we need to subtract the amount I’d pay today to satisfy the mortgage from the total payments I’d make if I didn’t pay off the mortgage today.

Let’s get to it.

Step 1:

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

N: (this is what I’m trying to find)

I/YR: 3.875

PV: 66,924.65

PMT: -352.16

FV: 0

When I plug these numbers into the calculator, I find that I have 295 payments left to make on this mortgage.

Step 2:

If I paid off the mortgage today, I’d avoid 295 payments, each of which is $352.16.

295 months times $352.16 per month is $103,887.20 I can avoid paying over the next 25ish years by paying $66,924.65 today.

Step 3:

I owe $66,924.65 which means any amount I pay above that is interest on the loan. My payments will add up to $103,887.20 so the amount of interest I’ll be paying on the loan over time will be $103,887.20 – $66,924.65 which is a total of **$36,962.55**. If I pay off the loan now, I’ll save **$36,962.55** in interest over time.

Note that doing this problem doesn’t tell me whether it’s a *good idea* to pay off the mortgage today, it just tells me how much interest I’d save if I decided to do so.

and Windows 7!

**THE SCENARIO**

I recently got a letter from the company that manages the 401(k) accounts at the place I used to work. They said that if their projections are correct, then when I retire (in 23 years), my account should provide $48,000 per year in income (amounts have been changed to protect the innocent). Wow, $4,000 per month to live on! Sounds great! (Actually, it sounds a little thin to me if that’s all the income I have, but we’ll go with it for now.)

However, I’ve heard of inflation, so what I want to know is ‘How much buying power, in today’s dollars, will that $4,000 per month have in 23 years?’

To keep things simple, I’ll use monthly compounding, and an inflation rate of 3.7%. (This is about what the average annual inflation rate has been in the United States for the past 40 years.)

If you don’t like my 3.7% number, feel free to use one you think better matches reality, or that better predicts the future. I got my figure here. Keep in mind that if you decide to use a different inflation figure, your answer will turn out different than mine.

**THE SOLUTION**

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

23 years is 23 x 12 months, which is 276 months.

N: 276

I/YR: 3.7

PV: (this is what I’m trying to find)

PMT: 0

FV: 4000

When I plug in the numbers, I find that my monthly stipend beginning in 23 years has the same buying power as **$1,710.19** today.

If I was questioning my living comfort after retirement on $4,000 per month, I’m *seriously* questioning it at less than half of that figure.

You may wonder ‘why does the calculator return a negative number for PV?’ (The calculator says that PV is -1,710.19.) The answer is that another way to consider this scenario is to ask yourself the question ‘How much would I have to invest today at 3.7% to get me $4,000 in 23 years?’ Since I’m going to *get* $4,000 in the future, I need to *invest* (i.e. pay out) some money today, so PV is represented as a negative number.

and Windows 7!

**THE SCENARIO**

If you’ve been [literally anywhere], you’ve no doubt run across people claiming that gold is the best investment, that the US Dollar (or most other currencies you could name) is a ‘fiat currency’, and that ever since the US fully went off the Gold Standard in 1971*, our money’s been worthless because it’s not backed by a metal you have to dig out of the ground… but that metal has *real, intrinsic, inherent* value.**

But let’s say that you had the foresight to buy an ounce of gold long ago, and you wanted to sell it today. How good would your return be?

A quick Internet search reveals that on March 13th 1975, gold was selling for $178.00 per ounce. I was just about to be born at the time, so let’s say that my parents bought me an ounce of gold to make me rich when I got older.

On May 14th 2017, it was going for $1,228.60.

If we use monthly compounding, what’s your return on investment if you bought an ounce of gold back in March of 1973?

* If you want to know more about gold as an investment, and about how and why the US and other countries left the gold standard, check out this awesome set of podcasts from NPR’s Planet Money.

** In case it’s not clear from my tone here, I don’t buy this argument for a second, and when I hear it, I wonder what the person making the claim is trying to sell me (or buy from me). Hint: if they’re willing to trade their ‘valuable’ gold for your ‘worthless’ dollars… maybe they’re not giving you the straight story. Anyway, enough editorializing. Back to the math.

**THE SOLUTION**

First off, we have to figure out how many months are between March 1975 and May 2017. Quick math reveals that there are 42 years and 2 months between those two points, which is 506 months. First thing first, we make sure the calculator is set to use 12 Payments per Year.

So we enter into the calculator:

N: 506

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

PV: -178.00

PMT: 0

FV: 1,228.60

Running the calculation, we find out that the return that lump of shiny yellow metal gave us is **4.37%** per year. Knowing that, does your opinion of the impressiveness of gold as investment change at all?

Knowing that inflation between 1975 and 2017 averaged 3.73%, does that change anything?

Anyway, good investing! See you next time!

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