Lorkay Seidens Inc. just borrowed $25,000. The loan is to be repaid in equal installments at the end of each of the next five years, and the interest rate is 10 percent.

1. Set up an amortization schedule for the loan._{(6 points)}
2. How large must each annual payment be if the loan is for $50,000? Assume that the interest rate remains at 10 percent and that the loan is paid off over five years.^{(2 points)}
3. How large must each payment be if the loan is for $50,000, the interest rate is 10 percent, and the loan is paid off in equal installments at the end of each of the next 10 years? This loan is for the same amount as the loan in part (2), but the payments are spread out over twice as many periods. Why are these payments not half as large as the payments on the loan in part (2)?_{(2 points)}

1. Using Financial Calculator

N= 5,I/Y= 10,PV= 25,000,andFV= 0;compute PMT=6,594.94.

1. Using Formula

^{PVA = PMT [{ \frac{1- \frac{1}{(1+r)^n}}r}] \)}

^{25,000 = PMT[3.79079]}

^{PMT = 6,594.94}

Set up an amortization schedule as described in the appendix to Chapter 9.

Amortization TableYear

Beginning

Balance

Payment

Interest*

Repayment

of Principal

Remaining

Balance

1$25,000.00$6,594.94$2,500.00$ 4,094.94$20,905.06220,905.066,594.942,090.514,504.4316,400.63316,400.636,594.941,640.064,954.8811,445.75411,445.756,594.941,144.585,450.365,995.3655,995.366,594.94599.545,995.400.00$32,974.69$7,974.69$25,000.00

*Interest equals 10 percent of the outstanding balance at the beginning of the year.

2.Here the loan size is doubled, so the payments also double in size to $13,189.87.

Using a financial calculator

N= 5,I/Y= 10,PV= 50,000, andFV= 0;compute PMT=-13,189.87

Notice the only difference from the computation of PMT in part (1) is that FV is twice as large ($50,000), so the payment (PMT) is double.

3.Using a financial calculator,

N= 10,I/Y= 10,PV= 50,000, andFV= 0;compute PMT=-8,137.27.

Because the payments are spread out over a longer time period, more interest must be paid on the loan. The total interest paid on the 10-year loan is $31,372.70 versus interest of $15,949.37 on the five-year loan; but the same $50,000 principal is repaid over a longer period, so the total payment per year is not doubled.