Question

Aviva deposited some amount of money at a 4% annual interest rate into her bank account. The money was left in the account for 18 months, and she did not make any more deposits. If Aviva's money earned $240 interest after 18 months, how much money did she deposit into the account?

Answer 1

To find out how much money Aviva deposited, we can use the formula for simple interest:

\[
I = P \times r \times t
\]

where:
- \( I \) is the interest earned (in dollars),
- \( P \) is the principal amount (the initial deposit),
- \( r \) is the annual interest rate (as a decimal),
- \( t \) is the time the money is invested for (in years).

From the problem, we know:
- \( I = 240 \)
- \( r = 4\% = 0.04 \)
- \( t = 18 \text{ months} = 1.5 \text{ years} \)

Now we can rearrange the formula to solve for \( P \):

\[
P = \frac{I}{r \times t}
\]

Substituting the known values into the equation:

\[
P = \frac{240}{0.04 \times 1.5}
\]

First, calculate \( r \times t \):

\[
0.04 \times 1.5 = 0.06
\]

Now, substitute this value back into the equation for \( P \):

\[
P = \frac{240}{0.06}
\]

Now we divide:

\[
P = 4000
\]

Thus, Aviva deposited **$4000** into her bank account.