Question

How long (in months) would it take to pay off a student loan totally $10,000 if a monthly payment of $300 is made each month and the appropriate rate of intrest is 4% annual rate compounded monthly?

38.0

33.4

35.4

46.7

43.0

Answer 1

Loan amount = $10,000

Monthly payment = $300

Calculating the no of months to pay off the Loan:-

Where, P = Loan amount = $10,000

r = Periodic Interest rate = 4%/12 = 0.3333%

n= no of periods

9*(1.003333)^n - 9 = (1.003333)^n

8*(1.003333)^n = 9

(1.003333)^n = 1.125

Taking Log on both sides,

n*Log(1.003333) = Log(1.125)

n*0.0014452409 = 0.051152522

n = 35.40

So, no of months it would take to pay off the loan is 35.40

Option 3

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