Question

. A recent mining engineering graduate wants to purchase a new car in 5 years which...

. A recent mining engineering graduate wants to purchase a new car in 5 years which presently costs $ 40,000 but the price of the car is rising at an annual compound rate of 12%. If he makes semiannual deposits to an account which pays 16 % compounded semiannually, how large must these payments be?

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Answer #1

Amount Req after 5 years = Current Price (1+i)5

Where i is inflation rate

= $ 40,000 * (1+0.12)5

= $ 40,000 * (1.12)5

= $ 40,000 * 1.7623

= $ 70,493.67

Thus FV of annuity shall be equal to $ 70,493.67

Here Payments are semi nnual

FV of Annuity = Cash flows * [ (1+r)n - 1 ] / r

where r is int rate per six months & n is no. of six months

$ 70,493.67 = Cash Flow * [ (1+0.08)10 - 1 ] / 0.08

= Cash Flow * [ (1.08)10 - 1 ] / 0.08

= Cash Flow * [ 2.1589 - 1 ] / 0.08

= Cash Flow * [ 1.1589 ] / 0.08

Cash Flow = 70,493.67 * 0.08 / 1.1589

= $ 4,866.25

Pls cmment, if any further assistance is required.

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