Question

How much would $20,000 due in 50 years be worth today if the discount rate were 7.5%?a. $438.03b. $461.08c. $485.35d. $510.89e. $537.78

Answer 1

The present value is $537.78

Step-by-step explanation:

Given

`Future\ Value\ (FV) = \$20,000\\Time (T) = 50\ Years\\Discount\ Rate\ (R)= 7.5\%`

Required

The Present Value(I)

To calculate the present value, we simply apply the formula for future value;

`FV = I *(1 + R)^T`

Substitute 20,000 for FV; 50 for T and 7.5% for R;

This gives

`20,000 = I *(1 + 7.5\%)^(50)`

Convert percent to decimal

`20,000 = I *(1 + 0.075)^(50)`

`20,000 = I *(1.075)^(50)`

`20,000 = I *37.19`

Divide both sides by 37.19

`(20,000)/(37.19) = (I *37.19)/(37.19)`

`(20,000)/(37.19) = I`

`537.778 = I`

`I = 547.78\ (Approximated)`

Hence, the present value is $537.78