Question

a $30000 5-year payment loan with level payment payable at the end of each month.

(i) Calculate the level payment of each month with loan interest of 8% effective monthly.

(ii) Calculate the loan balance at the end of month 3 after the third loan payment is made by using retrospective method.

(iii) Calculate the loan balance at the end of month 3 after the third loan payment is made by using prospective method.

(iv) what is total interest paid for the entire loan period.

Answer 1

Level payment = loan amount x pvaf

= 30000xpvaf(5,8%)

= 30000x3.9927=119781

Therefore per annum payment = 119781/5 = 23956.20

And per month payment = 23956.20/12 = $1996.35

(ii).  

Calculation of loan balance after 3rd month payment = 30000x(1+0.08/12)³ - 1996.35x[{1+0.08/12}³ - 1]/0.08/12

30000x1.0202-6029

=30606-6029=$24577.

Loan balance at the end of month 3 after 3rd month payment = $24577

(iii) . Calculation of loan balance at the end of month 3 after 3rd payment using prospective method will be as follows

Month	beginning of month balance	interest	payment monthly	principal payment	ending balance of month
1	30000	201	1996.35	1795.35	28204.35
2	28204.35	189	1996.35	1807.35	26397
3	26397	176.35	1996.35	1820	24577

Therefore balance of loan after 3rd payment using prospective method = $24577.

(iv) total interest payment = total payment - principal payment

= 119781-30000

= $89780