Question

a. What would be the annual payments on an 8 percent per annum installment loan of $1,000 with repayment over three years?

b. Write out the amortization schedule for the loan.

c. Now suppose that the payments were to be made on a semiannual basis: what would the semiannual payments be? Assume the 0.08 is a nominal rate.

d. Is the total paid in case (c) less or more than in the former case? Why?

Answer 1

- Loan Amount = $1,000

Interest rate = 8%

a). Calculating the annual payment of the loan:-

Where, P= Loan amount = $1000

r = Periodic Interest rate= 0.08

n= no of periods = 3

So, annual payment will be $ 388.03

b). Preparing the amortization schedule of the loan:-

Year	Beg bal.	Payment	Interest amount	Principal Amount	End Bal.
1	1,000.00	388.03	80.00	308.03	691.97
2	691.97	388.03	55.36	332.67	359.30
3	359.30	388.03	28.74	359.29	0.01

c). Now suppose that the payments were to be made on a semiannual basis.

Calculating the semi-annually payments:-

Where, P= Loan amount = $1000

r = Periodic Interest rate= 0.08/2 = 0.04

n= no of periods = 3yrs*2 = 6

So, semi-annual payment will be $ 190.76

d). Total amount made in annually payments = $388.03*3

= $1164.09

Total amount made in semi-annually payments = $190.76*6

= $1144.56

So, total paid as per semi-annual payments is less than paid as annual payments. Because interest is levied on outstanding balance and the more frequent you pay the less interest is to be paid. Thus, semi-annual payments are more frequent than annual payments. hence, there interest cost is less.

Concluding, Total paid as per semi-annual payments is less than paid as annual payments.

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