Question

A saving account opened 3 months ago now has a balance of Birr 20,400. If the bank pays 8% simple interest, how much money was deposited?

Answer 1

To find the initial amount deposited into the saving account, we can use the formula for simple interest:

\[
A = P + I
\]

where:
- \( A \) is the total amount in the account (balance),
- \( P \) is the principal or initial amount deposited,
- \( I \) is the interest earned.

The interest \( I \) can be calculated using the formula:

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

where:
- \( r \) is the rate of interest (as a decimal),
- \( t \) is the time the money is invested or borrowed for (in years).

In this case:
- \( A = 20,400 \) Birr
- \( r = 8\% = 0.08 \)
- \( t = 3 \) months = \( \frac{3}{12} = \frac{1}{4} \) years

Now, substituting \( t \) into the interest formula:

\[
I = P \times 0.08 \times \frac{1}{4} = P \times 0.02
\]

Now, we can plug \( I \) back into the equation for \( A \):

\[
A = P + I
\]
\[
20,400 = P + P \times 0.02
\]
\[
20,400 = P (1 + 0.02)
\]
\[
20,400 = P \times 1.02
\]

To find \( P \), we divide both sides by \( 1.02 \):

\[
P = \frac{20,400}{1.02}
\]
\[
P = 20,000
\]

So, the initial amount deposited was **Birr 20,000**.