Question

Your student loan, taken out five years ago, wa in the amount of $20,000 with the annual interest rate of 5% compounded monthly over those five years. Because it is a student loan, you did not make any payments until now. You just graduated and your payment starts at the end of each month starting at the end of this month. If you plan to pay back the loan in 5 years, how much is your monthly payment?

• $333.81
• $484.37
• $830.56
• $1,105.33
• None of the above

Answer 1

Given about student loan,

Loan of amount A = $20000 was take 5 year ago at interest rate r = 5% compounded monthly

No interest was paid till now.

So, value of loan now using compounding is

Present value of loan = A*(1 + r/n)^(n*t) = 20000*(1 + 0.05/12)^(12*5) = $25667.17

Now monthly payment will be paid on it for next 5 years starting end of this month

So, now this is an ordinary annuity and monthly payment can be calculated using formula

Monthly payment PMT = PV*(1 - (1+r/n)^(-n*t))/(r/n) = 25667.17*(1 - (1+0.05/12)^(-12*5))/(0.05/12) = $484.37

So, Monthly payment for this loan is $484.37

Option B is correct.