Using time value of money (TVM) calculations, how long must you stay in the house to breakeven on a $4,000 investment for a savings of $109.89 per month?

To find out how long you must stay in the house to break even on a $4,000 investment, given a savings of $109.89 per month, the time value of money (TVM) calculations should be applied. Specifically, you’ll be interested in determining how many months it takes for the cumulative savings to equal the upfront investment of $4,000.

The formula used in TVM calculations to find the future value of a series of cash flows (in this case, monthly savings) can be rearranged to solve for time. Since you're saving a fixed amount each month, you can treat this as an annuity where you want to determine how many payments equal the initial investment.

By taking the $4,000 investment and dividing it by the monthly savings of $109.89, you initially calculate how many total months it would take to simply recover the initial investment:

Total months = Investment / Savings per month = $4,000 / $109.89.

This results in approximately 36.4 months. However, this calculation assumes no interest earned on the investment.

When you factor in the savings accruing over those months, using the formula for the present value of annuities, a slight adjustment occurs, resulting in