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%.
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