Question

Yen is planning for her retirement. She is 30 years old today and would like to have RM800,000 when she turns 55. She estimates that she will be able to earn a 9% rate of return on her retirement investment over time; she wants to set aside a constant amount of money every year (at the end of the year) to help achieve her objective. How much money must she invest at the end of each of the next 25 years to realize her goal of RM800,000 at the end of that time?

Answer 1

To calculate the amount Yen needs to invest at the end of each year to reach her goal, we can use the formula for the present value of an annuity:

PV = PMT * ((1 - (1 + r)^(-n)) / r)

Where:

PV = present value (the amount Yen wants to have at retirement)
PMT = the constant annual payment (what Yen needs to invest each year)
r = the annual interest rate (9% in this case)
n = the number of years until Yen's retirement (25 years)

So, to find the PMT, we can rearrange the formula to:

PMT = PV / ((1 - (1 + r)^(-n)) / r)

Plugging in the given values:

PMT = 800,000 / ((1 - (1 + 0.09)^(-25)) / 0.09)

PMT = RM 16,939.22

Therefore, Yen must invest RM16,939.22 at the end of each year for the next 25 years to reach her goal of RM800,000 at retirement.