Question

 

Suppose you plan to borrow $300,000 from a financial institution and you are required to repay the loan by making equal annual payments for five years (payment at the end of each year). The interest rate for the loan is 3.5% per year. Show your answers correct to two decimal points.

1. Calculate the annual payment required.
2. Prepare an amortization schedule for the loan for each year according to the following format.

Year	Beginning balance	Annual payment	Interest paid	Principal paid	Ending Balance
1
2
3
4
5
Total

c. If instead, the loan is an interest-only loan, you are required to pay interest on the original loan amount at the end of each year for five years, and to repay the entire loan amount at the end of the loan period. Compute the total amount that you need to pay (interest plus loan amount) in the five-year period.

d. Ignoring part (c) above, if you are offered a constant amortizing loan, which is a loan where the annual amortization amount (principal paid) is constant throughout the loan period, which type of loan (equal annual payment or constant amortizing) would result in paying a greater amount of total interest over the life of the loan? Explain without actually calculating the interest.

Answer 1

Borrow Amount = $3,00,000

Rate of interest = 3.5% per year

A) Calculation of annual Payment required

PVIFA , 5year @ 3.5% = 4.515

therefor Annual payment = $3,00,000/4.515 = $ 66445.18/-

B) Amortisation Schedule

Year	Begning Balance	Annual Payment	Interest Paid	Principal Paid	Ending Balance
1	$300,000	$66,445.18	10500.00	$55,945	$244,055
2	$244,055	$66,445.18	8541.92	$57,903	$186,152
3	$186,152	$66,445.18	6515.30	$59,930	$126,222
4	$126,222	$66,445.18	4417.76	$62,027	$64,194
5	$64,194	$66,445.18	2251.18	$64,194	$0
Total		$332,226	$32,226	$300,000

C) Compute the total amount that you need to pay (interest plus loan amount) in the five-year period

Interest per year = $300000*3.5% = $10,500

Total interest in 5 year = $10500*5= $52500

Principal in 5th year to be paid = $ 300000

Total amount to be paid ie interest plus principal = $ 52500+$300000= $352500/-

D) if We paid Constant Pricipal over the 5 year than Amortisation schedule are as follows

Year	Begning Balance	Annual Payment	Interest Paid	Principal Paid	Ending Balance
1	$300,000	$70,500.00	10500.00	$60,000	$240,000
2	$240,000	$68,400.00	8400.00	$60,000	$180,000
3	$180,000	$66,300.00	6300.00	$60,000	$120,000
4	$120,000	$64,200.00	4200.00	$60,000	$60,000
5	$60,000	$60,000.00	2100.00	$60,000	$0
Total		$329,400	$31,500	$300,000