Question

Kyle decides to buy some equipment for his lawn mowing business. For this equipment, he must pay the following amounts:

a) Now $0 End of year 1: $10,000 End of Year 2: $8,500 End of year 3: $9,700 If the appropriate discount rate is of 12 percent p.a. compounding semi-annually, calculate the value of the equipment Kyle purchased, in today’s dollars.

b) Jack borrows $10,000 today to be paid off in three equal year-end amounts. The interest rate on the borrowing is 12% p.a. compounding annually. Complete the following amortisation schedule. (Show workings in the space below)

Year Balance beginning of year Annual Interest $

(to nearest cent) Repayment $ (to nearest cent)

Balance end of

year 1 $10000.00

2

3 $0

C) decide that I need $1.2 million in retirement savings by the time I turn 65. I am 30 years old today and commence depositing a regular yearly amount to my retirement savings account to achieve this goal. If my savings account can earn 7.2% per annum (effective), calculate the regular annual amount that I need to deposit (assume the first deposit is today and last deposit is when I turn 64).

Answer 1

a. Answer : $ 22,471.35

Effective annual interest rate at semiannual compounding = [ 1 + 0.12 / 2 ] ² - 1 ] = 12.36 %

Year	Cash Flows	PV factor at 12.36 %	Present Values
1	$ 10,000	0.8900	$ 8,900
2	8,500	0.7921	6,732.85
3	9,700	0.7050	6,838.50
			$ 22,471.35

b. PVIFA12%, n=3  = [ { 1 - ( 1 / 1.12 ) ³ } / 0.12 ] = 2.4018

Annual payment = $ 10,000 / 2.4018 = $ 4,163.54

Year	Balance, Beginning of Year	Annual Interest	Repayment	Balance, End of Year
1	$ 10,000	$ 1,200	$ 2,963.54	$ 7,036.46
2	7,036.46	844.38	3,319.16	3,717.30
3	3,717.30	446.24	3,717.30	0
			$ 10,000

c. Future Value of an Annuity = Annuity x Future Value Interest Factor of Annuity Due of $ 1 ( FVIFAD)

FVIFAD7.2%, n=35 = [ { ( 1.072) ³⁵ - 1 } / 0.072] * ( 1.072) = 144.4126 x 1.072 = 154.8103

Annual deposit required = $ 1,200,000 / 154.8103 = $ 7,751.42