Retirement Time Value of Money

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Junior (College 3rd year) ・Mathematics ・MLA

The age of mine as of first day of next month i.e. 01 August 2017 will turn into 20 years. I am considering a retirement age of 65 years, which leaves me with (65-20) = 45 years of investment for a healthy retirement. I would like to withdraw money for 25 years after retirement to continue to till 90 years of age. The total amount to be withdrawn per month is $500, i.e. $60,000 per year. Annual rate of interest is 7%.

The present value of money at age 64 that is to be withdrawn during age 65 to 90 can be calculate by the formula:

PV =

Here, Annual Withdrawal amount, P = $60,000

At 3% monthly inflation rate, this amount becomes, P = $126,901.17 ≈ $126,900

Total number of years, n = 25

Annual Interest rate, r = 7%

This gives, PV = $126,900 × ) = $1478839.70

Now, I am expecting to have this $1478839.70 amount at the end of the saving period, i.e. at the age of 65, which may be considered to be a future value, FV at the age of 20. I need to calculate the yearly payment, PMT for the period between 20 to 65 i.e. for a period of 45 years.

At the 2013 rate, the maximum federal social security income is $2,533 per month or $30,400 per year. Let us assume that the average pension paid by the HR of the job I would retire from is $1,800 per month or $21,600 per year. These leaves us with ($1478839.77–$30,400–$21,600) = 1426839.70 per year of saving.

FV = PMT

Here, FV = $1426839.70

Interest Rate, i = 12%

Number of years, n = 35

Rearranging the formula and plugging these values give,

PMT = = = $3305.42

Now,

Therefore, I need to save ($3305.42/12) = $275.45 per month in order to ensure a comfortable retirement.

Starting to save 5 years earlier would give a longer span of saving period, n =

FV = PMT

Here, FV = $1426839.70

Interest Rate, i = 12%

Number of years, n = 40

Rearranging the formula and plugging these values give,

PMT = = = $1860

Now,

Therefore, I need to save ($1860/12) = $155 per month in order to ensure a comfortable retirement.

So, starting 5 years earlier would reduce monthly saving to $155 from $275.45.

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