If you borrow $7,000 with an interest rate of 3 percent, to be repaid in five...

If you borrow $7,000 with an interest rate of 3 percent, to be repaid in five equal yearly payments at the end of the next five years, what would be the amount of each payment? Use Exhibit 1-D. (Round time value factor to 3 decimal places and final answer to 2 decimal places.)

Amount of each paymet

Expert Solution

Amount of each payment is $1528.48

Calculation of Annual Installment

Equated annual installment =			1 Divided BY (present value of annuity factor for 5 year at 3%)

i.e.			1 / present value of annuity factor for 5 year at 3%
			1 / present value of annuity factor for 5 year at 3%

Calculation of present value of annuity factor for 5 year at 3%
Annuity factor is the total of present value factor for 5 years at 3%

Year		Present value factor @ 3%
1		0.971
2		0.943
3		0.915
4		0.888
5		0.863
Total		4.580

Equated annual installment = $ 7,000/4.580
		= $1528.48


loan repayment schedule
Year	Opening balance of loan	Interest	Total loan	Installment	Balance of loan at the end of the year

1	$ 7,000.00	$ 210.00	$ 7,210.00	$ 1,528.48	$ 5,681.52
2	$ 5,681.52	$ 170.45	$ 5,851.96	$ 1,528.48	$ 4,323.48
3	$ 4,323.48	$ 129.70	$ 4,453.19	$ 1,528.48	$ 2,924.70
4	$ 2,924.70	$ 87.74	$ 3,012.45	$ 1,528.48	$ 1,483.96
5	$ 1,483.96	$ 44.52	$ 1,528.48	$ 1,528.48	$ -

Notes
Interest is calculated by charging interest at 3% on opening balance of loan each year
Interest for the year 5 is taken as balance of loan installment and opening balance of loan of year 5 (i.e. $ 1,528.482 - 1483.963). This is done so that balance of loan at the end of 5th is Nil.

jeff jeffy answered 6 months ago

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