Question

You have the option of buying an extended warranty for your car. The extended warranty costs $50 a month for 36 months. Included in the warranty is service for your car every 6 months valued at $75 each. Also included is the cost of any major repair. What is the present value of the included cost for major repair if the interest rate is 6% annual compounded monthly?

Answer 1

Interest rate is 6%/12 = 0.5% per month. Time is 36 months and cost of warranty is $50 a month. Savings are $75 per 6 month. The cost of repair is X in present value. Then, the present value cost should be equal to the present value benefits

50(P/A, 0.5%, 36) = X + 75((P/F, 0.5%, 6) + (P/F, 0.5%, 12) + (P/F, 0.5%, 18) + (P/F, 0.5%, 24) + (P/F, 0.5%, 30) + (P/F, 0.5%, 36)

50*32.8710 = = X + 75*(0.97502+0.94191+0.91414+0.88719+0.86103+0.83564)

This gives X = $1237.43