Math
posted by Kate on .
Henry bought a new dishwasher for $320. He paid $20 down and made 10 monthly payments of $34. What actual yearly interest did Henry pay?
1  14.55
2  29.09
3  34.38
4  68.75

Here is a quick approximate way to do it. Otherwise you need a much more complicated method, or some website that uses Java to do it for you.
(320  20)/2 = $150 was the average balance during payoff.
Total interest payments were (340320) = $20
(5/6 yr)* %150*I (per yr) = $20
I = 0.16 = 16%
It is actually a bit lower than that, because the average balance is a bit higher than $150. So I'd got with 14.55% 
Henry bought a new dishwasher for $320. He paid $20 down and made 10 monthly payments of $34. What actual yearly interest did Henry pay?
1  14.55
2  29.09
3  34.38
4  68.75
The monthly payment to pay off a loan derives from R = Pi/[1  (1+i)^n] where R = the monthly payment (or rent), P = the loan amount (or principal, n = the number of interest bearing periods and i = the yearly interest rate divided by 100(12).
R = 34
P = 300
i = I/100(12)annualized
n = 10 months
Therefore, 34 = 300i/[1  (1+i)^10].
By trial and error, I reached a yearly interest rate of 29.09%, or close enough for our purposes, 29% gives me a monthly payment of $34.13.
For 29%, i = .29/12 = .024166666...
R = 300(.024166666)/[1  1.024166666)^10] = $34.13 per month.
You can play around with the % to get exactly $34 if you wish.