Question

What is the difference in the present worth between an investment of $10,000 per year for 50 years and an investment of $10,000 per year forever at an interest rate of 10% per year

Answer 1

Difference in Present Value = $ 851.86

Step-by-step explanation:

The fist scheme is an annuity. A series of fixed cash flow occurring annually for certain period of time. We can determine the present value of the annuity using the formula below:

PV = A × (1- (1+r)^(-n) )/r

10,000 × (1- 1.10^(-50))/0.1 =99,148.14

The second scheme is a perpetuity . A series of fixed cash inflow occurring for the unforeseeable future

PV = A × 1/r

PV = 10,000× 1/0.1= 100,000

Difference in PV = 100,000 - 99,148.14= 851.855

Difference in Present Value = $ 851.86