Home / Money Blog

## Windfall Choices

Note: You can use any financial calculator to do this problem, but if you want the BEST, you can get our 10bii Financial Calculator for iOS, Android, Mac, and Windows!
Image Source
THE SCENARIO If I were to win, earn, or inherit \$200,000 (after taxes) all at once, I could do quite a bit with that money. I could buy several cars, upgrade my living situation, or take a mind-blowing vacation. However, if I wanted to use that money to set myself up for a comfortable retirement, I could do so in several different ways. Let's compare two of them. Option 1: Buying stocks I could invest the money into the S&P 500 index (this approach is recommended pretty commonly by financial advisors, so it must have some merit), and it might make an average annual return of 7.5%. Option 2: Buying rental property I could buy a rental house, and it might net me \$400 per month in rental income (after depreciation, property taxes, maintenance, management, and other expenses) and appreciate at a rate of 3% per year (assume it can be sold with no costs and no taxes at the end). While I'm renting the house for those 25 years, I'll take the \$400 per month in net rent and invest that in the S&P 500 where it would make the 7.5% annual return. The question: At the end of 25 years, which of these approaches will leave me with a larger lump sum of money?
THE SOLUTION This one has several parts, which are all pretty straightforward.
1. Determine the value of my simple S&P 500 purchase after it grows for 25 years
2. Determine the value of the rental property paired with the over-time S&P 500 purchase
1. Determine the value of the rental house after its appreciation
2. Determine the value of the S&P 500 investment that's being contributed to over time
3. Compare the two results
For reference, 25 years is 25 x 12 = 300 months. First things first, make sure the calculator is using 12 Payments per Year. Step 1: The lump-sum S&P 500 investment N: 300 (The investment will last for 25 years, which is 300 months) I/YR: 7.5 (We're assuming that the index fund will yield 7.5% per year) PV: -200,000 (I'm investing the whole \$200,000 into the stocks) PMT: 0 (During the 25 years, I'm not contributing or withdrawing anything) FV: (This is what I'm trying to find)

After 25 years, my stock account will be worth \$1,296,576.09.

Step 2.1: The house's appreciation N: 300 (The investment will last for 25 years, which is 300 months) I/YR: 3 (We're assuming that the house will appreciate 3% per year) PV: -200,000 (At the beginning, the house is worth \$200,000) PMT: 0 (The house's value doesn't have any monthly contributions or withdrawals) FV: (This is what I'm trying to find)

After 25 years, the house will be worth \$423,003.91.

Step 2.2: The over-time S&P 500 investment N: 300 (The investment will last for 25 years, which is 300 months) I/YR: 7.5 (We're assuming that the index fund will yield 7.5% per year) PV: 0 (Since I'm investing net rents, I have nothing at the beginning) PMT: -400 (I'm investing the \$400 per month in net rent from the rental house) FV: (This is what I'm trying to find)

The stock account with over-time purchases will have \$350,904.35 in it at the end.

Step 2.3: The house's total Adding up the house's value with the over-time stock account value, the buy-a-house approach will give me \$423,003.91 + \$350,904.35 = \$773,908.26 after 25 years. Step 3: Comparing the two If I bought the stocks with the whole lump sum up front, at the end I'd have \$1,296,576.09. On the other hand, the house approach yields me only \$773,908.26.

So the stocks-only approach would leave me with \$1,296,576.09 - \$773,908.26 = \$522,667.83 more than the house-and-stocks approach.

What do you think? Did you expect this answer? Does it make sense to you? Did I miss anything? Let us know in the comments!