# Math Help - Compound Interest

1. ## Compound Interest

Hey guys, i need with this.

To make $20,000 in 3 years, Sally decides to make 6 equal deposits in an account at 6-monthly intervals starting now. If the interest rate is 11% per annum compounded semi-annually, how much is each deposit? 2. Hello, Steve! To make$20,000 in 3 years, Sally decides to make 6 equal deposits
in an account at 6-monthly intervals starting now.
If the interest rate is 11% per annum compounded semi-annually,
how much is each deposit?

This is an Annuity problem.
If you're not familiar with the formula, you're in deep weeds . . .

Annuity formula: . $A \;=\;D\,\frac{(1+i)^n-1}{i}$

. . where: . $\begin{Bmatrix}A &=& \text{final amount} \\ D &=& \text{periodic deposit} \\ i &=& \text{periodic interest rate} \\ n &=& \text{number of periods} \end{Bmatrix}$

We have: . $A = 20,000,\; i = \frac{11\%}{2} = 0.055,\;n = 6$
. . and we might as well solve for $D\!:\;\;D \;=\;A\,\frac{i}{(1+i)^n-1}$

So we have: . $D \;=\;20,000\,\frac{0.055}{(1.055)^6-1} \;=\;2903.578952$

Therefore, Sally should deposit \$2903.58 each time.

3. ## I know there is a limit to be eligible for a grant

I am looking for a student grant if am going to college? I don't want any student loan because I can't pay it back. How much money you have to make per year to be eligible for the federal student aid grant? The grant you don't have to pay it back? I know there is a limit to be eligible for a grant. Does any body know? Or if there like a chart that showing how much money you make and how much money you get.