Suppose you borrowed $30,000 at a rate of 8.5% and must repay it in 5 equal installments at the end of each of the next 5 years.How much would you still owe at the end of the first year,after you have made the first payment?
A) $19,118.33
B) $22,112.76
C) $22,343.11
D) $23,034.13
E) $20,961.06

Question

Quizplus · Accepted Answer

The loan of $30,000 bears an annual interest rate of 8.5%, which is equivalent to 0.085 as a decimal. To determine the equal annual payments over the next 5 years that would fully amortize the loan, we can use the following formula:
PMT = r(PV)/(1-(1+r)^(-n))
where PMT is the equal annual payment, r is the annual interest rate, PV is the present value of the loan, and n is the number of payments. Plugging in the given values, we get:
PMT = 0.085($30,000)/(1-(1+0.085)^(-5)) = $7,618.34
Therefore, the borrower must make annual payments of $7,618.34 for the next 5 years.
At the end of the first year, the borrower will have made the first payment of $7,618.34. The remaining balance on the loan can be calculated by subtracting the portion of the payment that goes towards interest from the total payment, and then subtracting that amount from the previous balance. Using the following formula:
Interest = r * Previous Balance
Principal = PMT - Interest
New Balance = Previous Balance - Principal
Plugging in the given values, we get:
Interest = 0.085 * $30,000 = $2,550
Principal = $7,618.34 - $2,550 = $5,068.34
New Balance = $30,000 - $5,068.34 = $24,931.66
Therefore, the borrower would still owe $24,931.66 at the end of the first year after making the first payment.
The closest answer choice to this calculation is D) $23,034.13.

Suppose You Borrowed $30,000 at a Rate of 8