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.