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You are about to ask the bank for a loan for $ 5,000 at a compound...

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Finance

You are about to ask the bank for a loan for $ 5,000 at acompound annual interest rate of 9% with a monthly capitalization.You are asked to make five semiannual payments and that the firstpayment be made at the end of the first semester. For eachsemester, calculate the interest payment and the principalpayment.

Answer & Explanation Solved by verified expert
4.1 Ratings (651 Votes)

Loan amount = 5000
Interest rate annual is 9% compounded monthly.So monthly rate = 9%/12= 0.0075

Semiannual rate = ( (1+monthly rate)^no. of months in semiannual year) -1
((1+0.0075)^6)-1= 0.0458522351
Total semiannual periods = 5

Equal annual payments for loan formula = P* i *((1+i)^n)/((1+i)^n-1)

5000*0.0458522351*((1+0.0458522351)^5)/(((1+0.0458522351)^5)-1)
$1,141.66

So, interest and principal payment is calculated in following amortization table.

Loan amortization table
Year Beginning balance Payment Interest Principal payment Ending balance
(Beg. Bal.*0.0458522351) (Payment - interest)

(Beg. Balance - principal payment.)
1 5000.00 1141.66 229.26 912.40 4087.60
2 4087.60 1141.66 187.43 954.24 3133.36
3 3133.36 1141.66 143.67 997.99 2135.36
4 2135.36 1141.66 97.91 1043.75 1091.61
5 1091.61 1141.66 50.05 1091.61 0.00
Total 5708.32 708.32 5000.00

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