Question

Holly open to savings account at a local bank. She deposited $2, 300.00 into the account 10 years ago. If the account earns an annual simple interest rate of 5.5%, how much interest has she earned?

Answer 1

To determine the accrued amount on a savings account that earns an annual simple interest, you have to use the following formula:

$A=P(1+rt)$

Where

A is the accrued amount after a determined time period

P is the principal or initial amount in the account

r is the interest rate, expressed as a decimal value

t is the time period, expressed in years

The initial amount of the account was $2300.

The time period was 10 years.

The interest rate is R=5.5%, to express it as a decimal value you have to divide it by 100:

$\begin{gathered} r=\frac{R}{100} \\ r=\frac{5.5}{100} \\ r=0.055 \end{gathered}$

Replace the known values in the formula to determine the accrued amount:

$\begin{gathered} A=P(1+rt) \\ A=2300(1+0.055\cdot10) \\ A=2300(1+0.55) \\ A=2300\cdot1.55 \\ A=3565 \end{gathered}$

Now, the accrued amount (A) is equal to the sum of the initial amount (P) and the interest (I) earned after t time periods:

$A=P+I$

To determine the interest earned, you can subtract the initial amount from the accrued amount

$\begin{gathered} I=A-P \\ I=3565-2300 \\ I=1265 \end{gathered}$

So, after 10 years she earned $1265 of interest.