Question

. You would like to have enough money saved to receive a growing annuity for 20 years, growing at a rate of 5 percent per year, with the first payment of $50,000 occurring exactly one year after retirement. How much would you need to save in your retirement fund to achieve this goal? The interest rate is 10 percent.

Answer 1

Present Value= $312,966.57

Step-by-step explanation:

Giving the following information:

Annual cash flow= $50,000

Number of years= 20

Growing rate= 5%

Interest rate= 10%

To calculate the present value, first, we need to determine the final value. The easiest way to incorporate the growing rate is to add it tho the interest rate.

Interest rate= 10% + 5%= 15%

Now, using the following formula, we can determine the final value:

FV= {A*[(1+i)^n-1]}/i

A= annual pay

FV= {50,000*[(1.15^20)-1]} / 0.15= $5,122,179.13

The present value is:

PV= FV/(1+i)^n

PV= 5,122,179.13/ 1.15^20= $312,966.57