Question

Which of these expressions will give the unpaid balance after 6 years on a $90,000 loan with an APR of 7.2%, compounded monthly, if the monthly payment is $708.61?
A. 90,000(1+0.072)^72+708.61[1-(1+0.072)^72/0.072]
B. 90,000(1+0.006)^6+708.61[1-(1+0.006)^6/0.006]
C. 90,000(1+0.006)^72+708.61[1-(1+0.006)^72/0.006]
D. 90,000(1+0.072)^6+708.61[1-(1+0.072)^6/0.072]

Answer 1

Answer:

  none of the expressions shown is correct

  The appropriate expression is ...

     90,000(1+0.006)^72+708.61[(1-(1+0.006)^72)/0.006] . . . best matches C

Step-by-step explanation:

The formula used to calculate the remaining balance is ...

  A = P(1 +r)^n +p((1 -(1 +r)^n)/r) . . . . . note the parentheses on the fraction numerator

In this formula, r is the monthly interest rate: 7.2%/12 = 0.006, and n is the number of monthly payments: 6×12 = 72. Putting these values into the formula along with the loan amount (P=90,000) and the payment amount (p=708.61) gives ...

  A = 90,000(1.006)^72 +708.61((1 -(1.006)^72)/0.006)

  A = 74,871.52