Question

# You are saving for retirement. To live​ comfortably, you decide you will need to save \$3,000,000...

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.)

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.

#### Earn Coins

Coins can be redeemed for fabulous gifts.