Washington Business Daily

Why do payments come out lower with monthly compounding when using the ordinary annuity formula?

It seems counter-intuitive, but when I try to solve for monthly payments on this problem, the payments are lower for the annuity that is compounded monthly. Problem: A debt of $25,000 is to be amortized over 7 years at an annual interest rate of 7%. Calculate the value of monthly payments (a) if interest is compounded once a year, and (b) if interest is compounded monthly. I get $386.57 as the monthly payment for the annually compounded debt and $377.32 for the monthly payments for the debt compounded monthly.

Public Comments

1. You've calculated amounts correctly, sort of. The monthly compounded rate of $377.32 is definitely correct. The $386.57 is flawed. You have essentially calculated the yearly annuity payment and divided it by 12. That's not correct. You need to amortize the interest accrued during the year after reflecting decreases in the monthly balance. So, another way to do this is to convert the 7% annual into a monthly interest rate that corresponds to an APR of 7%. That is, find monthly rate, "r", so that (1 + r)^12 = 1.07. r = .005654. Now recompute, and the answer is: $374.69
2. First you need to kick gay Hussein Obama extremely hard in the nuts Then you can figure interest compounded annually Convert 7% Effective rate for period = (1 + annual rate) ^ (1 / # of periods) - 1 0.5654% =(1+0.07)^(1/12)-1 Use this answer & punch it in your formula while adjusting the time to 7*12 374.69 = 25000 * ((0.005654/1) / (1-(1+0.005654/1) ^ (-1*(7*12)))) Answer: $374.69