Question

Diane opened a savings account 3 years ago the account earns 9% interest compounded monthly if the current balance is 100.00 how much did she despoit initially

Answer 1

Answer:

The amount she deposited initially is $76.41.

$\text{ \ 76.41}$

Explanation:

We want to find the amount of Principal she deposited initially.

Recall that the formula for calculating the Principal of a compound interest is;

$P=\frac{A}{(1+\frac{r}{n})^{nt}}$

Where;

P = Principal / initial amount

A = Future/ final amount

r = Interest rate (decimal)

n = number of times the interest is compounded per year.

t = Time in years

From the question, we were given the following;

A = $100.00

r = 9% = 0.09

n = monthly (12 months in a year) = 12 times

t = 3 years

Substituting the given values into the formula, we have;

$\begin{gathered} P=\frac{100.00}{(1+\frac{0.09}{12})^{12(3)}} \\ P=\frac{100.00}{(1+0.0075)^{36}} \\ P=\frac{100.00}{(1.0075)^{36}} \\ P=76.41 \\ P=\text{ \ 76.41} \end{gathered}$

Therefore, the amount she deposited initially is $76.41.

$\text{ \ 76.41}$