Question

Your client is 30 years old . She wants to begin saving for retirement with the first payment to come one year from now. She can save $3,000 per year, and you advise her to invest it in the stock market, which you expect to provide average return of 10% in the future.

a. If she follows your advice, how much will she have at 60?
b. She expects to live for 20 yrs if she retires. If her investment earns 6% return, how much will she be able to withdraw at the end of each year after retirement?

Answer 1

If she saves $3,000 per year for 30 years and earns an average return of 10%, she will have approximately $52,347 saved at age 60. if she expects to live for 20 years after retirement and earns a 6% return on her investments she will be able to withdraw approximately $3,717.12 at the end of each year after retirement.

Step-by-step explanation:

To answer these questions, we need to calculate the future value of the investments using compound interest.

a. If she saves $3,000 per year for 30 years and earns an average return of 10%, the future value of her investments at age 60 can be calculated using the formula for compound interest: Future Value = Present Value * (1 + Interest Rate)^Number of Years. In this case, the present value is $3,000 per year, the interest rate is 10%, and the number of years is 30. Plugging in these values:Future Value = $3,000 * (1 + 0.10)^30 = $3,000 * 17.449 = $52,347. So, she will have approximately $52,347 saved at age 60 if she follows your advice.

b. If she expects to live for 20 years after retirement and earns a 6% return on her investments, we can calculate the amount she can withdraw each year using the formula for the future value of an annuity: Withdrawal Amount = Future Value / [(1 + Interest Rate)^Number of Years - 1]. In this case, the future value is $52,347, the interest rate is 6%, and the number of years is 20. Plugging in these values:Withdrawal Amount = $52,347 / [(1 + 0.06)^20 - 1] = $52,347 / 14.0789 = $3,717.12. So, she will be able to withdraw approximately $3,717.12 at the end of each year after retirement.