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 (340-320) = $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.
$34.38
To calculate the actual yearly interest Henry paid, we need to find the total amount he paid in interest over the course of one year.
First, let's calculate the total amount he paid for the dishwasher. He paid $20 down, and then made 10 monthly payments of $34.
So the total amount he paid for the dishwasher is:
$20 (down payment) + 10 * $34 (monthly payments) = $20 + $340 = $360
Now, let's calculate the interest paid. The interest paid is the difference between the total amount paid for the dishwasher ($360) and the cost of the dishwasher ($320).
Interest paid = $360 - $320 = $40
Since Henry made 10 monthly payments, the yearly interest paid would be 12 times the monthly interest.
Monthly interest paid = $40 / 10 = $4
Yearly interest paid = $4 * 12 = $48
Therefore, the actual yearly interest that Henry paid is $48.
None of the provided options (1 - 14.55, 2 - 29.09, 3 - 34.38, 4 - 68.75) match the correct answer of $48.