Question

You are saving for retirement. To live comfortably, you decide you will need to save $3,000,000 by the time you are age 65. Today is your 27th birthday, and you decide, starting today and continuing on every birthday up to and including your 65th birthday, that you will put the same amount into a savings account. If the interest rate is 10 %, you set aside $ 7473 each year to make sure that you will have $3,000,000 in the account on your 65th birthday. You realize that your plan has a flaw. Because your income will increase over your lifetime, it would be more realistic to save less now and more later. Instead of putting the same amount aside each year, you decide to let the amount that you set aside grow by 12 % per year. Under this plan, how much will you put into the account today? (Recall that you are planning to make the first contribution to the account today.)

Answer #1

**If we have $3,000,000 at the age of 65
then,**

**when interest rate is 10%, which are compounded
annually, then installment for the same is -**

**Future value = Present value ( 1 + r
) ^{n}**

**$3,000,000 = Present value ( 1 + 10/100 ) ^{(65 -
27)}**

**Present value = $3,000,000 / ( 1 +
0.1) ^{38}**

**Present Value = $ 3,000,000 / 37.4043434**

**Present value = $ 80,204.589**

**If he contribute $ 80,204.589 at the interest rate of
10% then, at the age of 65, he has $3,000,000.**

**If the interest rate is 12%, then amount to be
contributed per year to have $3,000,000 at the age of
65.**

**$3,000,000 = Present value ( 1 +
12/100) ^{38}**

**Present value = $3,000,000 / ( 1 +
0.12) ^{38}**

**Present value = $3,000,000 / 74.1796639**

**Present value = $ 40,442.351**

**If he invest $ 40,442.351 at the interest rate of 12%
per year he can get $3,000,000 at the age of 65.**

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