To determine how much money the man needs to deposit today in order to have N150,000 after three years at a compound interest rate of 25%, we can use the formula for compound interest. The formula is: \[ A = P(1 + r)^n \] Where: - \( A \) is the amount of money accumulated after n years, including interest. - \( P \) is the principal amount (the initial amount of money). - \( r \) is the annual interest rate (decimal). - \( n \) is the number of years the money is invested or borrowed. ### Step-by-Step Solution 1. **Identify the variables**: - We know \( A = 150,000 \) (the amount he wants after 3 years). - The interest rate \( r = 25\% = 0.25 \). - The time period \( n = 3 \) years. 2. **Rearranging the formula**: We need to find \( P \), so we rearrange the formula to solve for \( P \): \[ P = \frac{A}{(1 + r)^n} \] 3. **Substituting the values**: Now we substitute the known values into the rearranged formula: \[ P = \frac{150,000}{(1 + 0.25)^3} \] 4. **Calculating \( (1 + r)^n \)**: First, calculate \( (1 + 0.25)^3 \): \[ (1 + 0.25) = 1.25 \] \[ (1.25)^3 = 1.25 \times 1.25 \times 1.25 \] - First, calculate \( 1.25 \times 1.25 = 1.5625 \). - Then, multiply \( 1.5625 \times 1.25 = 1.953125 \). 5. **Calculating \( P \)**: Now substitute back into the equation for \( P \): \[ P = \frac{150,000}{1.953125} \] Performing the division: \[ P \approx 76,800.00 \] ### Conclusion Thus, the amount the man needs to deposit today is approximately **N76,800.00**. ### Explanation of Options - **Option A: N112,000.50** - This amount is too high. If he deposited this amount, he would end up with much more than N150,000 after three years. - **Option B: N96,000.00** - This is also too high. Similar to option A, this would yield more than N150,000. - **Option C: N85,714.28** - This amount is still higher than necessary. It would also result in more than N150,000 after three years. - **Option D: N76,800.00** - This is the correct answer, as calculated above. ### Revision Summary - Use the compound interest formula \( A = P(1 + r)^n \) to find the principal. - Rearrange the formula to solve for \( P \): \( P = \frac{A}{(1 + r)^n} \). - Calculate \( (1 + r)^n \) carefully to avoid errors. - Substitute values accurately to find the required deposit amount. This thorough understanding of the compound interest formula and careful calculations will help in similar problems in the future.