Question

In: Accounting

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

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.

Solutions

Expert Solution

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


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