Question

. 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?

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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