I am promised a payment of $250 a year from now, repeating every year for a total of ten years. I can invest money at 10% interest, but the inflation rate over the next ten years is expected to be 5%. What is the smallest amount of money you could offer me right now that would persuade me to give up these payments?
A)250(P/A,0.05,10)
B)250(P/A,0.15,10)
C)250(A/P,0.1,10)
D)250(P/A,0.155,10)
E)250(P/A,0.165,10)

Question

Quizplus · Accepted Answer

The correct answer involves adjusting the interest rate for inflation to find the real interest rate using the formula $r = \frac{1+i}{1+f} - 1$, where $r$ is the real interest rate, $i$ is the nominal interest rate, and $f$ is the inflation rate. With $i = 0.10$ and $f = 0.05$, we get $r = \frac{1.10}{1.05} - 1 = 0.047619$ or approximately 4.76%. However, the correct approach to find the present value of the annuity considers the Fisher equation for adjusting nominal rates to real rates in the presence of inflation, which wasn't applied directly here. Instead, the closest option that accounts for both the interest and inflation in a simplified manner is option D, which suggests a higher rate than the nominal interest rate to account for inflation indirectly, although the exact calculation for the real interest rate adjustment wasn't directly applied. The correct interpretation should involve calculating the present value of an annuity using a rate that reflects both the time value of money (interest rate) and the decrease in money's purchasing power (inflation rate). The options provided don't directly reflect the precise calculation for adjusting for inflation, but option D is chosen as it suggests a compounded effect that could approximate considering both factors.

I Am Promised a Payment of $250 a Year from Now