# Math Help - Series, Annuties

1. ## Series, Annuties

if you deposit $1000 in your bank account yearly, and earn 5% interest per year, what is the formula for the nth term of this series? 2. Hi Each year your money is multiplied by 1.05 At the end of year n, you have got $1000 \cdot 1.05^n$ 3. I tried this but it doesn't work, because after each year the 5% of interest has been added to the account plus the deposited$1000, and another 5% on interest is added t o this value. For example, after year 1 there is $1050 in the account to which another additional$1000 is added to make $2050, and the interest is added to get$2152.50.

4. Hello, hsidhu!

If you deposit \$1000 in your bank account yearly, and earn 5% interest per year,
what is the formula for the $n^{th}$ term of this series?
I assume you mean the balance at the end of $n$ years.

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

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

We have: . $D = 1000,\;i = 0.05$, and $n$ periods.

Therefore: . $A \;=\;1000\cdot\frac{(1.05)^n-1}{0.05}$