1. ## Finite Math: Annuities!

Im having problems trying to figure out how to solve this problem.

The formula for Future Value of an Ordinary Annuity is

FV=PMT( (1+I)^n -1)/I)

The problem isFind the I (rate per period) and the N( number of Periods) for each annuity.

Quarterly deposits of $500 are made for 20 years into an annuity that pays 8% coumpounded quarterly. fv=500((1+.08/4)^20-1)/.08 Since it is deposited quarterly do i multiply 500x4? and since it is compounded quarterly do I divide both interest by 4? help! thanks 2. Originally Posted by lunaj fv=500((1+.08/4)^20-1)/.08 should be fv=500((1+.08/4)^(20*4)-1)/(.08/4) 3. Thanks! When a question says that a certain amount is deposited x number of times a year, do i ignore that and just divide the interest and multiply n by the # compunded?? In this case$500 is deposited quarterly and the whole thing is coumpounded quarterly, so it all works out to 4.

what if $500 is deposited every month and coumpounded quarterly? 4. Originally Posted by lunaj When a question says that a certain amount is deposited x number of times a year, do i ignore that and just divide the interest and multiply n by the # compunded?? Kinda Originally Posted by lunaj In this case$500 is deposited quarterly and the whole thing is coumpounded quarterly, so it all works out to 4.

what if $500 is deposited every month and coumpounded quarterly? Then you have a complex or general annuity problem. You need to convert the quarterly rate into its equivalent monthly rate. One way of doing this is to equate the effective rate of say 8% compounded quarterly as given by$\displaystyle
w_{{\text{compounded quarterly}}} = \left( {1 + \frac{{.08}}
{4}} \right)^4 - 1
$with the effective rate of j% compounded monthly which is given by$\displaystyle
w_{{\text{compounded monthly}}} = \left( {1 + \frac{j}
{{12}}} \right)^{12} - 1
\$
You then solve for j.
After that, you merely replace 8% with j and 4 with 12 in your corrected formula.

5. Do do both of these for one problem?

ex

500( 1+.08/12)^12-1/.08/12 and then i multiply this answer the same way but compunded quarterly?

im confused

6. Originally Posted by lunaj
Do do both of these for one problem?

ex

500( 1+.08/12)^12-1/.08/12 and then i multiply this answer the same way but compunded quarterly?

im confused
should be
500[( 1+j/12)^(20*12)-1]/(j/12)
but you must first equate the right hand side of

with the right hand side of

and solve for j.