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Question 2 of 6 Christopher's student loan of $23,000 at 2.82% compounded quarterly was amortized over 6 years with payments made at the end of every month. What was the principal balance on the loan after 4 years? Round to the nearest cent Submit Question Next Question

Answer 1

First, we calculate the effective annual rate (EAR) of the loan.

EAR = (1 + (APR/n))ⁿ - 1

where APR = nominal annual rate

n = number of compounding periods per year. This is 4, as the compounding is quarterly.

EAR = (1 + (2.82%/4))⁴ - 1

EAR = 2.85%

Next, we calculate the APR such that with monthly compounding, the EAR equals 2.85%. With monthly compounding, n = 12.

EAR = (1 + (APR/n))ⁿ - 1

2.85% = (1 + (APR/12))¹² - 1

APR = (((1 + 0.0285)^1/12) - 1) * 12

APR = 2.8134%

Now, we calculate the principal paid off after 4 years (48 months) using CUMPRINC function in Excel :

rate = 2.8134%/12 (converting APR into monthly rate)

nper = 6*12 (6 year loan with 12 monthly payments each year)

pv = 23000 (original loan amount)

start period = 1 (We are calculating principal paid off between 1st and 48th month)

end period = 48 (We are calculating principal paid off between 1st and 48th month)

type = 0 (each payment is made at the end of month)

CUMPRINC is calculated to be $14,898.64

A8 =CUMPRINC(A7/12,6*12,23000,1,48,0) B C D 7 A 2 .8134% 8 | $(14,898.64)!

The balance loan principal outstanding after 4 years =  $23,000 - $14,898.64 = $8,101.36