Question

Terrell opened a savings account 10 years ago. The account earns 9% interest, compounded annually. If the current balance is $300.00, how much did he deposit initially? Round your answer to the nearest cent.

Answer 1

1) Gathering the data

Time: 10 yrs ago

Interest rate (r) : 9% (0.09)

Future Value: 300

Initial Deposit:?

2) Since the current balance is given, let's call it Future Value because the amount that made that $300 is what we need to find out. Let's go find the Future Value since it's been 10 yrs ago. Plugging into the formula we have:

$\begin{gathered} F=P(1+r/n)^{nt} \\ 300=P(1+\frac{0.09}{1})^{1\cdot10} \\ 300=P(1.09)^{10} \\ 300=2.367363675P \\ P=\frac{300}{2.367363675} \\ P=126.723 \\ P\cong126.72 \end{gathered}$

Notice that, since this investment was compounded yearly, so n=1.

3) So the initial deposit, 10 years ago was approximately $126.72