Suppose you start saving for retirement when you are 45 years old. You invest $5,000 the first year and increase this amount by 3% each year to match inflation for a total of 20 years. The interest rate is 10% per year. How much money will you have saved when you are 65 years old

FV= $404,734.15

Explanation:

Giving the following information:

Annual investment (A)= $5,000

Increase rate= 3%

Interest rate= 10%

Number of periods= 20 years

To simplify calculations, we will sum up the increased rate to the interest rate. The effect on the investment of both rates is the same.

Real interest rate= 0.03 + 0.1= 0.13

Now, to determine the nominal value of the account in 20 years, we need to use the following formula:

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

A= annual deposit

FV= {5,000*[(1.13^20) - 1]} / 0.13

FV= $404,734.15

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