Sachi buys a couch and a love seat for $4800. She pays $500 and finances the rest at $156.54 per month for 3 years. What annual interest rate, compounded monthly, is Sachi being charged? Round your answer to two decimal places.
$4,800 - $500 = $4,300 Amount Financed.
PMT=PV. R.{[1 + R]^N/ [1 + R]^N - 1}
$156.54 =$4,300.R{[1 + R]^36 / [1 + R]^36 - 1}
P.S. There is no DIRECT or algebraic way of solving for interest rate. However, iteration and interpolation are used to get closer and closer to the actual rate. After doing that half a dozen times, I got: 1.5416667 per month or: 1.5416667 x 12 =18.5% compounded monthly.
May I ask, what type of calculator do you have? It should have these keys:
N I%YR PV PMT FV
Make sure N is in MONTHS for this problem. Enter 36 under N.
Enter $4,300 under PV
Enter zero(0) under FV
Enter $156.54 under PMT. You may have to make it negative or -$156.54.
Solve for I%YR. It should give you the interest rate per month. Just multiply by 12 to give you annual interest rate compounded monthly. Depending on the calculator, it may give you annual interest rate.
Just try it and see if you get the same rate that I got above. Good luck.
+956 @Guest
I'm not sure if you're the same human who keeps helping me, but you have helped me sooo much! Thank you :)
+118608 Julius, I tried using your calculator and it refused to work out the nominal (or any other) interest rate.
Maybe you'd do better with a different calculator. :/
+118608 Hi again Julius,
I just tried a different calculator and it would not do it either.
You may have to leave out the Payment and then 'guess' the interest rate, you guess will get closer and closer until it is within the desired 2 decimal places.
I shall try it with your calculator....
PV = 4800-500 = 4300
Periods = 36
monthly
FV=0
The PMT that you want is $156.64 but you cannot put that in.
You have to try different rates (these are nominal annual rates) until you find the one that will give you a PMT of $156.64.
| nominal annual rate tested % | PMT (payment found) | |
| 10 | 138.75 | Too little |
| 15 | 149.06 | Too little |
| 18 | 155.46 | Too little |
| 19 | 157.62 | Too big |
| 18.5 | 156.54 | Too little |
| 18.55 | 156.64 | exact |
So to two decimal places the nominal rate is 18.55% and that is using your calculator :)
