Your client is 40 years old, and she wants to begin saving for retirement, with the first payment to come one year from now. She can save RM5,000 per year, and you advise her to invest it in the stock market, which you expect to provide an average return of 9 percent in the future.
a. If she follows your advice, how much money would she have by 65? b. How much would she have at 70? c. If she expects to live for 20 years in retirement if she retires at 65 and her investment continue to earn the same rate (9 percent), how much could she withdraw at the end of each year after retirement age? (hint: calculate PMT)
ahihi
To calculate the answers to these questions, we can use a financial calculation called the future value of an annuity. For each scenario, we will use the formula:
FV = PMT * [(1 + r)^n - 1] / r
Where:
FV is the future value of the investment
PMT is the annual payment or contribution
r is the interest rate per period
n is the number of periods
Let's calculate each scenario step by step:
a. To determine how much money she would have by age 65, we can use the formula with the following values:
PMT = RM5,000
r = 9% (0.09 as a decimal)
n = 65 - 40 = 25 years (since she starts at age 41 and wants to accumulate until age 65)
Plugging in these values, we have:
FV = RM5,000 * [(1 + 0.09)^25 - 1] / 0.09
Calculating this, we find that she would have approximately RM309,607 by age 65.
b. To determine how much she would have at age 70, we again use the formula but adjust the number of years since she will be saving for an extra 5 years. So the values would be:
PMT = RM5,000
r = 9% (0.09 as a decimal)
n = 70 - 40 = 30 years
Plugging in these values, we have:
FV = RM5,000 * [(1 + 0.09)^30 - 1] / 0.09
Calculating this, we find that she would have approximately RM509,730 by age 70.
c. To determine how much she can withdraw annually during retirement, we can use a calculation called the present value of an annuity. This will help us determine the withdrawal amount that can be sustained over a period of time.
The present value of an annuity formula is:
PMT = PV * [r(1 + r)^n] / [(1 + r)^n - 1]
We need to rearrange this formula to solve for PV (present value) since we have the PMT, r, and n values from the previous calculations. Let's assume that she would like to withdraw funds for 20 years during her retirement.
PMT = Withdrawal amount per year
r = 9% (0.09 as a decimal)
n = 20 years
Plugging in these values, we have:
PMT = PV * [0.09(1 + 0.09)^20] / [(1 + 0.09)^20 - 1]
To solve for PV, we can rearrange the formula:
PV = PMT * [(1 + r)^n - 1] / [r(1 + r)^n]
Plugging in the values, we get:
PV = Withdrawal amount * [(1 + 0.09)^20 - 1] / [0.09(1 + 0.09)^20]
For example, if she wants to withdraw RM30,000 per year during retirement, we would use:
PV = RM30,000 * [(1 + 0.09)^20 - 1] / [0.09(1 + 0.09)^20]
Calculating this, we find that the present value of her retirement savings allows her to withdraw approximately RM329,493 annually for 20 years.
It's important to note that these calculations assume no additional contributions or changes in investment returns over time. It's always recommended to consult a financial advisor for personalized advice.