You want to buy a new sports car 3 years from now, and you plan to save $4,200 p

Question

You want to buy a new sports car 3 years from now, and you plan to save $4,200 per year, beginning one year from today. You will deposit your savings in an account that pays 5.2% interest. How much will you have just after you make the 3rd deposit, 3 years from now?

You just inherited some money, and a broker offers to sell you an annuity that pays $5,000 at the end of each year for 20 years. You could earn 5% on your money in other investments with equal risk. What is the most you should pay for the annuity?

Explanation / Answer

a) We have to find FV of $ 4000 deposited each year for 3 years starting one year from today, at the end of 3 years. Interest rate is 5.2% FV = 4000*1.052^2 + 4000*1.052 +4000 = 12634.82 ($) (ANSWER) b) annuity amount, a = $ 5000, interest rate, i = 5%, and maturity, n = 20 years The most that can be paid is PV of above annuity, PV = a*r*(1-r^n)/(1-r), where r = DF = 1/(1+i) = 1/1.05 PV = 5000*(1/1.05)*(1-(1/1.05)^20)/(1-1/1.05) => = 62311.05 ($) (ANSWER)

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