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?
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.
Hello, hsidhu!
I assume you mean the balance at the end of $\displaystyle n$ years.If you deposit $1000 in your bank account yearly, and earn 5% interest per year,
what is the formula for the $\displaystyle n^{th}$ term of this series?
Annuity Formula: .$\displaystyle A \;=\;D\,\frac{(1+i)^n-1}{i}$
. . where: .$\displaystyle \begin{Bmatrix}
A &=& \text{final balance} \\ D &=& \text{periodic deposit} \\ i &=& \text{periodic interest rate} \\ n &=& \text{number of periods} \end{Bmatrix}$
We have: .$\displaystyle D = 1000,\;i = 0.05$, and $\displaystyle n$ periods.
Therefore: .$\displaystyle A \;=\;1000\cdot\frac{(1.05)^n-1}{0.05} $