A student takes out a loan with an interest rate of 13.9% per annum, compounded annually. The amortization period is 1 year. If the finance charge is $800.00, what was the principal?

Question

$5179.86

$5755.40

$6330.94

$6906.47

Answer 1

To find the principal, we can use the formula for compound interest:

FV = PV(1 + r)^n

Where:
FV = Future Value (Principal + Finance Charge)
PV = Present Value (Principal)
r = annual interest rate
n = number of compounding periods

In this case, we know:
FV = PV + $800.00
r = 13.9% = 0.139
n = 1 (since it's compounded annually)

Substitute these values into the formula:

PV + $800.00 = PV(1 + 0.139)^1
PV + $800.00 = 1.139PV
$800.00 = 0.139PV
PV = $800.00 / 0.139
PV = $5755.40

Therefore, the principal was $5755.40.

The correct answer is:
$5755.40