Question

EZ Leifer plans to retire at the age of 65 and believes he will live to be 90. EZ wants to receive an annual retirement payment of $43,000 at the beginning of each year. He sets up a retirement account that is estimated to earn 6.8 percent annually. How much money must Easy have in the account when he reaches 65 years old?

Answer 1

Easy have to gave $510,410 in the account when he reaches 65 years old.

Explanation:

We have to calculate this with the annuity formula.

The amount of money that EZ has to have at the moment of retirement (65 years old) is the capital that will generate the annual payments until he is 90 years old.

The amount of payments will be 90-65=25 years.

The annuity formula for the capital, in function of the annual payment and the interest rate is:

`C=P\cdot ((1-(1+r)^(-n))/(r))\\\\C=43,000\cdot (1-(1.068)^(-25))/(0.068)=43,000\cdot (1-0.193)/(0.068)=43,000\cdot (0.807)/(0.068)\\\\\\C=43,000\cdot 11.87=510,410`