A friend offered to pay you $3,000 for each of the next three years beginning one year from now, $5,000 for each of the succeeding three years, and a lump sum of $10,000 one year thereafter. The interest rate is 10%. How much are these expected future sums worth today?
A)$30,909
B)$21,935
C)$17,447
D)None of the above

Question

Quizplus · Accepted Answer

To find the present value of the future payments, we need to discount each payment back to the present using the given interest rate of 10%.

For the first three years:
PV = 3000/(1+0.10)^1 + 3000/(1+0.10)^2 + 3000/(1+0.10)^3
PV = 8181.82

For the next three years:
PV = 5000/(1+0.10)^4 + 5000/(1+0.10)^5 + 5000/(1+0.10)^6
PV = 11333.01

For the lump sum payment in four years:
PV = 10000/(1+0.10)^4
PV = 6830.68

Adding the present values of each payment:
8181.82 + 11333.01 + 6830.68 = 26035.51

Therefore, the expected future sums are worth $26,035.51 today. Only option B is close to the calculated value.

A Friend Offered to Pay You $3,000 for Each of the Next