Question

a/ A piece of machinery depreciates in value by 5% a year. Determine its value in 3 years’
time if its current value is $50 000.

b/ Simon decides to buy a new sofa which is available at each of three stores at the same
fixed price. He decides to borrow the money using each store’s credit facility.
Store A has an effective rate of interest of 12.6%.
Store B charges interest at a rate of 10.5% compounded continuously.
Store C charges interest at a rate of 11.5% compounded quarterly

c/Determine the monthly repayments needed to repay a $125 000 loan which is paid back
over 20 years when the interest rate is 7% compounded annually. Round your answer to
2 decimal places.

Answer 1

Solution :-

(A)

Value after year 1 = $50,000 * ( 1 - 0.05 ) = $47,500

Value after year 2 = $47,500 * ( 1 - 0.05 ) = $45,125

Value after year 3 = $45,125 * ( 1 - 0.05 ) = $42,868.75

or the answer can be

Value after year 3 = $50,000 - $50,000 * 5% * 3 = $42,500

(b)

A = Effective rate per year = 12.6%

B = Effective rate per year = e ^10.5% - 1 = 1.1107 - 1 = 11.07%

C = Effective rate per year = ( 1 + 0.115 / 4 )⁴ - 1 = ( 1.02875 )⁴ - 1 = 1.1200 = 12.00%

Therefore Store B is to be Choosen

(c) Interest Rate monthly = ( 1 + 0.07 )¹² - 1 = 1.005654 = 0.5654%

Total Payment = 12 * 20 = 240

Monthly Repayment = $125,000 / PVAF ( 0.5654% , 240 )

= $125,000 / 128.98

= $969.11

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