Christina finances a piano for $3,070 by taking out an installment loan for 24 months. The payments were $153.50 per month and the total finance charge was $614. After 14 months, Christina decided to pay off the loan. After calculating the finance charge rebate, find her loan payoff.

Answer 1

I assume this is compound interest, since the time is more than 1 year.

We don't know the interest rate, let the monthly rate be i
then:
153.5(1 - (1+i)^-24)/i = 3070

a very tough equation to solve, I will use Wolfram:
http://www.wolframalpha.com/input/?i=153.5(1+-+(1%2Bx)%5E-24)%2Fx+%3D+3070
to get i = .0151308 (---> annual rate compounded monthly = 18.2%)

amount owing after 14 months = 3070(1.0151308)^14 =3788.32
value of 14 payments = 153.50(1.0151308^14 - 1)/.0151308 = 2373.70

amount owing = 3788.32 - 2373.70 = 1414.62

btw, the $614 total finance charge is bogus and has nothing to do with this.
If this is "simple interest" , then it would show an interest rate of 10%, totally misleading
since the true annual interest rate is over 18%