Question

Your grandmother would like to share some of her fortune with you. She offers to give you money under one of the following scenarios (you get to choose):

1. $7,000 a year at the end of each of the next eight years
2. $45,000 (lump sum) now
3. $75,000 (lump sum) eight years from now
Calculate the present value of each scenario using a 6% interest rate. Which scenario yields the highest present value? Would your preference change if you used a 12% interest rate?

Answer 1

The present value of each scenario is calculated using a 6% interest rate, with Scenario 1 yielding the highest present value. If a 12% interest rate is used, Scenario 3 would have the highest present value.

Step-by-step explanation:

To calculate the present value of each scenario, we need to use the formula for present value:

Present Value = Future Value / (1 + Interest Rate)n

Using the formula with a 6% interest rate:

Scenario 1: $7,000 a year for 8 years = $7,000 / (1+0.06)1 + $7,000 / (1+0.06)2 + ... + $7,000 / (1+0.06)8 = $39,726.45

Scenario 2: $45,000 lump sum = $45,000 / (1+0.06)8 = $28,151.18

Scenario 3: $75,000 lump sum in 8 years = $75,000 / (1+0.06)8 = $49,661.92

Therefore, Scenario 1 yields the highest present value of $39,726.45.

If we use a 12% interest rate instead, the present value calculations would be:

Scenario 1: $7,000 a year for 8 years = $7,000 / (1+0.12)1 + $7,000 / (1+0.12)2 + ... + $7,000 / (1+0.12)8 = $34,734.76

Scenario 2: $45,000 lump sum = $45,000 / (1+0.12)8 = $17,756.68

Scenario 3: $75,000 lump sum in 8 years = $75,000 / (1+0.12)8 = $30,163.72

Therefore, in this case, Scenario 3 yields the highest present value of $30,163.72.