Question

Trixie is considering buying a new car at a cost of $13931. She is planning to keep the car for five years and is hoping the car will sell for $3534 at the end of year 5. She estimates that insurance, fees, maintenance, and gas will be $1199 in year 1 and will gradually increase every year by $200. What is the equivalent uniform annual worth (EUAW) of this car at a 2% interest rate?

Answer 1

Present Value = PV = $13931

Salvage Value = SV = 3534

n = 5 years

r = 2% = 0.02

Let us draw the casf inflows and outflows for these 5 years to understand the cash flows -

To find out the Annual worth, let us first consider the Present Value of the cash flows -

PV = 13931 + 1199/1.02 + 1399/1.02² + 1599/1.02³ + 1799/1.02⁴ - 3534/1.02⁵

= $16,419

Annuity Factor A(t,r) = (1 - (1 / (1 + r)^t)) / r = (1-(1/1.02⁵))/0.02 = 4.71

Hence, Annual worth = 16419/4.71 = $3,486