Henry intends to retire in 14 years and would like to receive $2472 every six months for 19 years starting on the date of his retirement. How much must Henry deposit in an account today if interest is 6.65% compounded semi-annually?

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- Mar 14th 2007, 12:57 PM #1

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- Mar 14th 2007, 02:39 PM #2

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Hello, Julie!

You need a couple of important formulas for this problem.

If you don't know them, I don't see how you can expect to solve it.

Henry intends to retire in 14 years and would like to receive $2472

every six months for 19 years starting on the date of his retirement.

How much must Henry deposit in an account today

if interest is 6.65% compounded semi-annually?

Upon his retirement, he must have*A*dollars investing in a "sinking fund".

It will earn 6.65% interest compounded semi-annually and allow him to

withdraw $2472 every six months for 19 years before the funds are depleted.

. . . . . . . . . . . . . . . . . . .(1 + i)^n - 1

The formula is: . A . = . D·----------------

. . . . . . . . . . . . . . . . . . . i(1 + i)^n

. . where:*A*= amount invested,*D*= periodic withdrawl,

*i*= periodic interest rate,*n*= number of periods.

. . . . . . . . . . . . . . . . . . . (1.03325)^{38} - 1

We have: . A . = . 2472·------------------------------- . ≈ . $54,374.53

. . . . . . . . . . . . . . . . . (0.03325)(1.03325)^{38}

He must have this amount to invest upon his retirement.

Hence, he must deposit a certain amount (P) now.

The compound interest formula is: . A .= .P(1 + i)^n . → . P .= .A/(1 + i)^n

We have: .i = 0.03325, n = 28, A = 54,374.53

. . Hence: . P . = . 54,374.53/(1.03325)^{28} . ≈ . $21,759.25

- Mar 14th 2007, 04:00 PM #3

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