Question

# You have the option of buying an extended warranty for your car. The extended warranty costs...

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?

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

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