Derek decides to buy a new car. The dealership offers him a choice of paying $585.00 per month for 5 years (with the first payment due next month) or paying some amount today. He can borrow money from his bank to buy the car. The bank requires a 5.00% interest rate. What is the most that he would be willing to pay today rather than making the payments? SHOW FINANCIAL CALCULATIONS AND EQUATIONS, ROUND 2 DECIMALS
| Amount to be paid today will be present value of future payment. | ||||||||||||||||
| Present Value of future payments | = | Periodical payments*Present value of annuity of 1 | ||||||||||||||
| = | $ 585.00 | * | 52.99019 | |||||||||||||
| = | $ 30,999.26 | |||||||||||||||
| Working: | ||||||||||||||||
| Present value of annuity of 1 | = | (1-(1+i)^-n)/i | Where, | |||||||||||||
| = | (1-(1+0.004167)^-60)/0.004167 | i | = | 5%/12 | = | 0.004167 | ||||||||||
| = | 52.9901917 | n | = | 5*12 | = | 60 | ||||||||||
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