Question

1. Would you rather receive: $15,000 in three years, $1,000 per year for 20 years or $2000 per year for 15 years if the discount rate is 20%?

2. Why?

Answer 1

Discount Rate = 20%

Option 1:

$15,000 in 3 years

Present Value = $15,000/1.20^3
Present Value = $8,680.56

Option 2:

$1,000 per year for 20 years

Present Value = $1,000/1.20 + $1,000/1.20^2 + ... + $1,000/1.20^20
Present Value = $1,000 * (1 - (1/1.20)^20) / 0.20
Present Value = $1,000 * 4.86958
Present Value = $4,869.58

Option 3:

$2,000 per year for 15 years

Present Value = $2,000/1.20 + $2,000/1.20^2 + ... + $2,000/1.20^15
Present Value = $2,000 * (1 - (1/1.20)^15) / 0.20
Present Value = $2,000 * 4.67547
Present Value = $9,350.94

You should choose Option 3 as its Present Value is highest.