Question

Nico makes annual end-of-year payments of $5,043.71 on a four-year loan with an interest rate of 13 percent. The original principal amount was ________.

a) $15,000
b) $20,000
c) $25,000
d) $30,000

Answer 1

The original principal amount of the loan is approximately -$28,066.56.

Step-by-step explanation:

To find the original principal amount of the loan, we can use the formula for annuities:

PV = PMT * (1 - (1 + r)^-n) / r

Where PV is the present value or principal amount of the loan, PMT is the annual payment, r is the interest rate per period, and n is the number of periods. In this case, the annual payment is $5,043.71, the interest rate is 13% (or 0.13), and the loan term is 4 years.

Plugging these values into the formula:

PV = $5,043.71 * (1 - (1 + 0.13)^-4) / 0.13

Simplifying the equation:

PV = $5,043.71 * (1 - 1.7244) / 0.13 = $5,043.71 * (-0.7244) / 0.13 = -$5,043.71 * 5.5738

Thus, the original principal amount of the loan is approximately -$28,066.56.