SOLUTION: A 42-mounth loan to pay your car has monthly payments of R411.35.if interest rate is 8.1% compounded monthly, find the unpaid balance emmediately after the 24th payment.

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Question 1076757: A 42-mounth loan to pay your car has monthly payments of R411.35.if interest rate is 8.1% compounded monthly, find the unpaid balance emmediately after the 24th payment.
Found 2 solutions by jorel1380, MathTherapy:
Answer by jorel1380(3719) (Show Source):
You can put this solution on YOUR website!
To find the amount of the loan, we need to use the formula P = L[c(1 + c)^n]/[(1 + c)^n - 1], where P is the payment, L is the loan value,c is the monthly interest rate, and n is the number of monthly payments. So, we know:
411.35=L[((.081/12)(1+(.081/12))^42]/[((1+(.081/12))^42)-1]
411.35=L(0.02742351273982901235438391550962)
L=15000
The next formula is used to calculate the remaining loan balance (B) of a fixed payment loan after p months.
B = L[(1 + c)^n - (1 + c)^p]/[(1 + c)^n - 1]
So:
B=15000[((1+.081/12)^42 - ((1+.081/12)^24))]/[(1+.081/12)^42 -1]
B=15000[0.17870786510489822337008495708463]/[0.32650474474014464353606497832299]
B= R 8210.043 as the remaining balance. ☺☺☺☺

Answer by MathTherapy(10552) (Show Source):
You can put this solution on YOUR website!
A 42-mounth loan to pay your car has monthly payments of R411.35.if interest rate is 8.1% compounded monthly, find the unpaid balance emmediately after the 24th payment.

Upon AMORTIZING the $15,000 loan, $8,049.82 of the PRINCIPAL has been paid, leaving a balance of
This makes all the sense in the world, since the loan has passed the -way mark of years.
FYI: The 24th payment signifies 2 years of payment.