Question

Francisco has a savings account balance of $2,033.88. The interest rate on the account is 2.9% compounded monthly. If he opened the account nine years ago, what was the value of his initial deposit?

Answer 1

first draw the cash flow diagram

Answer 2

The formula to solve this is
\[A=P(1+\frac{r}{n})^{tn}\]
where A is the amount after t years, P is the initial deposit, r is the annual interest rate as a decimal and n is the number of compounding events per year.
Plugging in values we get
\[2033.88=P(1+\frac{0.029}{12})^{9\times 12}=P \times 1.0024167^{108}\]
Therefore wse can find P from
\[P=\frac{2033.88}{1.0024167^{108}}=you\ can\ calculate\]