Question

Amortization Schedule

Consider a $15,000 loan to be repaid in equal installments at the end of each of the next 5 years. The interest rate is 7%.

1. Set up an amortization schedule for the loan. Do not round intermediate calculations. Round your answers to the nearest cent. If your answer is zero, enter "0".

   Year	Payment	Repayment Interest	Repayment of Principal	Balance
   1	$	$	$	$
   2	$	$	$	$
   3	$	$	$	$
   4	$	$	$	$
   5	$	$	$	$
   Total	$	$	$

2. How large must each annual payment be if the loan is for $30,000? Assume that the interest rate remains at 7% and that the loan is still paid off over 5 years. Do not round intermediate calculations. Round your answer to the nearest cent.

   $  

3. How large must each payment be if the loan is for $30,000, the interest rate is 7%, 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 b, but the payments are spread out over twice as many periods. Do not round intermediate calculations. Round your answer to the nearest cent.

   $  

Why are these payments not half as large as the payments on the loan in part b?

I. Because the payments are spread out over a longer time period, more principal must be paid on the loan, which raises the amount of each payment.
II. Because the payments are spread out over a longer time period, less interest is paid on the loan, which raises the amount of each payment.
III. Because the payments are spread out over a longer time period, less interest is paid on the loan, which lowers the amount of each payment.
IV. Because the payments are spread out over a shorter time period, more interest is paid on the loan, which lowers the amount of each payment.
V. Because the payments are spread out over a longer time period, more interest must be paid on the loan, which raises the amount of each payment.

Answer 1

a) We are given the following information:

Payment	PMT	To be calculated
Rate of interest	r	7.00%
Number of years	n	5.00
Loan amount	PV	15000.00

We need to solve the following equation to arrive at the required PMT

So the annual payment is $3658.36

Amoortization schedule is as foolows:

Year	Opening Balance	PMT	Interest	Principal repayment	Closing Balance
1	$            15,000.00	$         3,658.36	$         1,050.00	$                     2,608.36	$         12,391.64
2	$            12,391.64	$         3,658.36	$             867.41	$                     2,790.95	$           9,600.69
3	$              9,600.69	$         3,658.36	$             672.05	$                     2,986.31	$           6,614.38
4	$              6,614.38	$         3,658.36	$             463.01	$                     3,195.35	$           3,419.03
5	$              3,419.03	$         3,658.36	$             239.33	$                     3,419.03	$                  -0.00
		$       18,291.80	$         3,291.80	$                   15,000.00

Opening balance = previous year's closing balance
Closing balance = Opening balance-Principal repayment
PMT is calculated as per the above formula
Interest = 0.07 x opening balance
Principal repayment = PMT - Interest

b)We are given the following information:

Payment	PMT	To be calculated
Rate of interest	r	7.00%
Number of years	n	5.00
Loan amount	PV	30000.00

We need to solve the following equation to arrive at the required PMT

So the annual payment is $7316.72

c)We are given the following information:

Payment	PMT	To be calculated
Rate of interest	r	7.00%
Number of years	n	10.00
Loan amount	PV	30000.00

We need to solve the following equation to arrive at the required PMT

d) These payments not half as large as the payments on the loan in part b?

I. If more principle must be paid then the PMT should be higher, so this is not the correct option

II. Interest paid per payment is higher because loan is paid over a longer period of time so this is not the correct option

III. This option correctly identifies all aspects and therefore is the correct option

IV. Payments are not spread over a shorter period

V. Although more interest is paid but the PMT is not as high as half of the PMT in part b