Compound interest and future value

Question

My van cost 120,000 at 6 percent interest for 5 years. Payments are due at the end of each month, and interest is compounded monthly. How much should I budget for the monthly payment? What formula would I use for this?

Answer 1

You should use the future value of an annuity formula

FV=(PMT*(1+i)ⁿ-1)/i

You then substitute in the known variables and solve for PMT:

120,000=(PMT*(1+6%/12)^5*12-1)/(6%/12)

PMT=120,000/(1+6%/12)^5*12-1)/(6%/12)

Then you simplify

PMT=120,000/(1+0.5%)⁶⁰-1)/0.5%

Your final answer is 1,719.936 which rounds to $1,719.94

Answer 2

=PMT(0.06/12,60,120000,,0)

This is Excel's function to calculate a payment amount:

6/12 gives us the monthly interest rate

5*12 gives us the number of payments

120,000 is the principle we will be paying

"0" tells Excel that the payment is at the end of each period, instead of the beginning

Happy calculating.