future value calculation

Question

Mr. Lim is 25 years old today; he is beginning to plan for his retirement as he intends to set up an account and make regular payments into it. Hence, He intends to set aside an equal amount at the end of each year for the next twenty-five years, so that he can retire at the age of fifty. He expects to live to the maximum age of seventy. He intends to withdraw RM25, 000 per year from the account on his 51st through his 70th birthdays. The account is expected to earn ten percent per annum for the entire period of time. Determine the size of annual deposits that by Mr. Lim must made.

Answer 1

This is a two-phase time value of money problem:

Accumulation phase (age 25–50, 25 deposits)

Withdrawal phase (age 51–70, 20 withdrawals of RM25,000 PER YEAR,

Ignores Taxes impact in calculations

Interest rate = 10% per year. (assumes constant 10% for all periods)

Step 1: Amount needed at age 50

At retirement (age 50), the account must contain enough to fund 20 annual withdrawals of RM25,000 starting at age 51.

This is the present value of an ordinary annuity at age 50:

PV=25,000×(1-(1.10)^(-20))/0.10

(1.10)^(-20)≈0.1486

PV=25,000×(1-0.1486) / 0.10

PV=25,000×8.514

PV≈212,850

So, RM212,850 is required at age 50.

Step 2: Annual deposits needed (age 25–50)

Now we determine the annual deposit required to accumulate RM212,850 in 25 years at 10%.

Use the future value of an ordinary annuity formula:

FV=A×(1.10)^25 - 1 / 0.10

(1.10)^25≈10.835

FV=A×(10.835-1)/0.10

FV=A×98.35

Set equal to required amount:

A×98.35=212,850

A=212,850/98.35

A≈2,164

Mr. Lim must deposit approximately: RM2,164 per year

At the end of each year for 25 years to fund his retirement withdrawals.