# Help!!!

• Mar 14th 2007, 12:57 PM
julie
Help!!!
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?
• Mar 14th 2007, 02:39 PM
Soroban
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.

Quote:

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
julie
Thanks
I used a different formula and my answer was different by 1,479.84.
this is the formula i used:
PV= PMT[ 1- (1+i)^-n]/i