$50,000 is borrowed, to be repaid in three equal, annual payments with 10% interest.Approximately how much principal is amortized with the first payment?
A)$201.06
B)$500.00
C)$1,510.57
D)$2,010.57

Question

Quizplus · Accepted Answer

To find the amount of principal amortized with the first payment, we need to first calculate the total amount of each payment.

Using the formula for the future value of an annuity:

PMT = PV x (i / (1 - (1 + i)^(-n)))

where 
PMT = the annual payment
PV = the present value (the amount borrowed)
i = the annual interest rate (10%)
n = the number of payments (3)

PMT = 50000 x (0.10 / (1 - (1 + 0.10)^(-3))) = $21,405.68

So each of the three payments will be $21,405.68.

To find the amount of principal amortized with the first payment, we need to subtract the interest from the payment.

For the first payment, the interest is calculated as:

Interest = PV x i = 50000 x 0.10 = $5,000

So the amount of principal amortized with the first payment is:

Principal = Payment - Interest = $21,405.68 - $5,000 = $16,405.68

Approximately, this is $1,510.57, which is choice C.

$50,000 Is Borrowed, to Be Repaid in Three Equal, Annual