Question

Prepare a schedule showing the amortization of a $12,000 loan to be repaid in 10 end-of-year installments that include interest at a rate of 6%. Jared and Courtney Jill own a parcel of fertile farm land which a local farmer has offered to rent for a period of 10 years. He is willing to make a payment of $20,000 today or pay an ordinary annuity of $3,400 at the end of each of the next 10 years. Which payment method should Jared and Courtney accept if the appropriate rate of return is 9%? A group of five faculty members at a Midwest University have recently purchased several acres near the school. They plan to gravel it and rent the parking spaces to commuting students. The cost of the project is $100,000. They paid $25,000 cash and are financing the balance with a note at 7.0% annual interest to be paid off in five equal annual payments with the first payment to be made at the end of the first year. The rental receipts are to be placed in an account for future improvements and cannot be used to repay the loan. If the annual payments are shared equally, how much would each member need to contribute annually to pay off the loan?

Answer 1

Solution :- (1)

Loan Amount = $12,000

Interest Rate = 6%

Total Payment ( Yearly ) = 10

Value of Installment = $12,000 / PVAF ( 6% , 10 )

= $12,000 / 7.3601

= $1630.42

	Amortization Table
Years	Opening Balance	Installment	Interest	Principal	Closing
1	$12,000	$1,630.42	$720	$910	$11,090
2	$11,090	$1,630.42	$665	$965	$10,125
3	$10,125	$1,630.42	$607	$1,023	$9,102
4	$9,102	$1,630.42	$546	$1,084	$8,017
5	$8,017	$1,630.42	$481	$1,149	$6,868
6	$6,868	$1,630.42	$412	$1,218	$5,650
7	$5,650	$1,630.42	$339	$1,291	$4,358
8	$4,358	$1,630.42	$261	$1,369	$2,989
9	$2,989	$1,630.42	$179	$1,451	$1,538
10	$1,538	$1,630.42	$92	$1,538	($0)

Here Interest = Opening Balance * 6%

Principal = installment - Interest

Closing = Opening - Principal

Solution :- 2

Alternative 1 :-

Annuity Payment = $3,400

Interest Rate = 9%

Time = 10

Present Value of Annuity = A * PVAF ( 9% , 10 )

= $3,400 * PVAF ( 9% , 10 )

= $3400 * 9.1743

= $31,192.66

Alternative 2 :-

One time payment = $20,000

Therefore Jared and Courtney accept Alternative 1 of annutiy of 10 years , as it has high present value as compared to other option .

Solution :- 3

Cost of Project = $100,000

Amount Financed = $100,000 - $25,000 = $75,000

Interest Rate = 7.0%

Total Payment = 5

Value of Annual installment = $75,000 / PVAF ( 7% , 5 )

= $75,000 / 4.1002

= $18,291.80

Amount shared by each = $18,291.80 / 3 = $6,097.27

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