An individual is currently 30 years old and she is planning her financial needs

Question

An individual is currently 30 years old and she is planning her financial needs upon retirement. She will retire at age 65 (exactly 35 years from now) and she plans on funding 20 years of retirement with her investments. Ignore any social security payments and ignore any taxes. She made $140,000 last year and she estimates she will need 75% of her current income in today's dollars to live on when she retires. She believes that inflation will average 2 percent per year during her working years. (For simplicity we will ignore inflation during her retirement years). She will retire at age 65 and will begin drawing down her retirement annuity at age 65. She plans on making a total of 20 annual withdrawals after she retires. After she retires she believes she will be able to earn 5.5 percent per year. If she puts her money in a blended stock and bond portfolio now, she figures she can earn 10.5 percent per year until she retires.

Retirement Planning

1.

value:
3.00 points

Required information

1) How much money will she need to withdraw each year starting at age 65 to have the same purchasing power as today? Round your answer to the nearest penny, do not enter the dollar sign in your answer.

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2.

value:
3.00 points

Required information

2) How much money must she have at age 65 in order to make her planned withdrawals? Round your answer to the nearest penny and do not enter the dollar sign in your answer.

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3.

value:
3.00 points

Required information

3) How much should she save per year starting right now in order to have the retirement annuity she desires? Round your answer to the nearest dollar and do not enter the dollar sign in your answer.

Explanation / Answer

So towards Part 1, we know that she will need 75% of her current income after her retirement each year to maintain the same level of purchasing power. That gives us her annual withdrawals after retirements to equal:

$140,000*75% = $105,000.

However, we have to find out what this sum would be worth 35 years from now (or when she's 65 years of age). This should be simple to calculate. We will find out the value of this sum 35 years from now compounded at 2%. This can be expressed as:

$105,000*(1+inflation)^35,

$105,000*1.02)^35,

$105,000*1.998= $209,790.

That is how much she will need to have on her retirement to maintain the same purchasing power.

Note: You can either look up the discounting factor in the discounting value tables, or you can calculate it with the following formula:

(1+i)^1) + (1+i)^2 + (1+i)^3.. + (1+i)^n, where n will denote the number of years, starting from year 1 until the final payment.

Part 2

Now we know that she requires $209,790 each year for 20 years after 35 years from now and we need to show what corpus she must have built in 35 years to sustain this payment for 20 years.

This would mean that we need to discount these withdrawals back by 20 years at the interest rate she would make after her retirement, which is given as 5.5%.

The Present Value of 20 payments for the withdrawal sums compounded annually will be given as:

$209,790*Discounting Factor of Annuity for 20 years at 5.5%,

=$209,790*11.9504=$2,507,070.74

Also, the discounting factor calculated here can be calculated in the same way as demonstrated above.

Part 3

So we found out how much she would require to have saved by the time she retires, but now we must find out how much she must save right now to build up that retirement corpus. Also, we know that this corpus will fetch an average return of 10.50%. Since this stream will also represent an annuity, the calculation can be given using the following expression:

PV = FV/Annuity discounting factor for 35 years at 10.50%

Present value of savings = $2,507,070.74/336.0955

= $7,459.40.

She will have to invest $7,459.40 per year beginning now for 35 years to maintain 75% of her current income at the time of her retirement. Also, the discounting factor calculated here can be calculated in the same way as demonstrated above.

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