Question

4 years ago, you made a student load of $20,000 with the annual interest rate of 8% compounded monthly. Because it is a student loan, you did not make any payments until now. You just graduated and your payment start at the end of each month (assume that today is 1st of the month). If you plan to pay back in 10 years, how much is your monthly payment?

a. $331.60

b. $333.81

c. $330.13

d. $327.94

Answer 1

b. $333.81

Working:

Step-1:Calculation of total outstanding amount of loan along with unpaid interest

Total amount outstanding as of today

=

P*(1+i)^n

P

$       20,000

=

20000*(1+0.00666667)^48

i

8%/12

=

0.00666667

=

$ 27,513.33

n

4*12

=

48

Step-2:Calculation of monthly payment

Monthly Payment

=

Total Amount outstanding / Present value of annuity of 1

=

$ 27,513.33

/

82.4215

=

$       333.81

Working:

Present Value of annuity of 1

=

(1-(1+i)^-n)/i

Where,

=

(1-(1+0.00666667)^-120)/0.00666667

i

0.00666667

=

82.4215

n

10*12

=

120