Question

Find the amount that an investor should deposit in a bank today if he needs Birr 20,000 in 3 months at a simple interest rate of 9%.

Answer 1

To find the amount that an investor should deposit today (the present value) if they need Birr 20,000 in 3 months at a simple interest rate of 9%, you can use the formula for simple interest:

\[
A = P(1 + rt)
\]

Where:
- \( A \) is the amount of money accumulated after n months, including interest.
- \( P \) is the principal amount (the initial deposit).
- \( r \) is the annual interest rate (decimal).
- \( t \) is the time the money is invested for, in years.

In your case:
- \( A = 20,000 \) Birr (the amount needed in 3 months).
- \( r = 9\% = 0.09 \) (annual interest rate).
- \( t = \frac{3}{12} = 0.25 \) years (since 3 months is 1/4 of a year).

We need to rearrange the formula to solve for \( P \):

\[
P = \frac{A}{1 + rt}
\]

Substitute the known values into the formula:

\[
P = \frac{20000}{1 + (0.09 \times 0.25)}
\]
\[
P = \frac{20000}{1 + 0.0225}
\]
\[
P = \frac{20000}{1.0225}
\]
\[
P \approx 19507.69
\]

Thus, the investor should deposit approximately Birr **19,507.69** today to have Birr 20,000 in 3 months at a simple interest rate of 9%.