Question

You are looking to purchase a new car, and you expect to have annual maintenance costs to keep it running. According to your calculations, you expect to incur $150 maintenance costs in the first year and expect the costs to increase by $75 for the next 7 years. You plan to keep the car for 8 years in total. How much money should you have in your savings account today, so that you do not have to worry about maintenance? The savings account pays 2% per year, compounded annually.

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Answer #1

Maintenance cost in the 1^{st} year = $150 (A1)

Increases by $75 every year (G)

Life = 8 years

Rate of interest = 2%

Calculate the present value (money should you have in your savings account today, so that you do not have to worry about maintenance)

First convert the gradient cash flow series into uniform cash flow series

A = A1 + G (A/G, 2%, 8)

A = $150 + $75 (3.3961) = $404.7

Present Value = $404.7 (P/A, 2%, 8)

Present Value = $404.7 (7.3255)

Present Value = $2,964.6 or $2,965 (rounded off to nearest $)

You should have $2,965 in your savings account today, so that you do not have to worry about maintenance.

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