Question

is the average annual rate of return you earned on your investment? You just won first place in a CUNY essay writing contest, and as your prize, you will receive $400 a month each month for the next 7 years (NOT $4,800 per year but $400 per month). If you can earn 8.25% per year on your money, what is the total prize worth to you today? 15. Your oldest child needs a car and you believe you can afford no more than $360 a month for a 5-year car loan. If the interest rate on this loan is 3.4% percent, what is the maximum you can afford to borrow to purchase this car?

Answer 1

Amount received each month = P = $400

Number of months = 7*12 = 84 months

Interest rate = 0.0825/12 monthly

PV = P/(1+r) + P/(1+r)² +....+ P/(1+r)ⁿ = P[1- (1+r)^-n]/r = 400[1- (1+0.0825/12)^-84]/(0.0825/12) = $25459.77

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Monthly Amount that can be paid = P = $360

Number of periods = 5*12 = 60 months

Interest rate = r = 0.034/12 monthly

Hence, Loan Amount = PV of all future Payments = P[1- (1+r)^-n]/r = 360[1- (1+0.034/12)^-60]/(0.034/12) = $19838