To determine the amount of money that a man deposited in his savings account, given the time period and interest rate, we can use the simple interest formula. Here's a step-by-step breakdown of the solution:
1. Identify the given information:
- Time period (T): 5 years
- Annual interest rate (R): 14%
- Interest earned (I): GH₵ 3500.00
2. Convert the annual interest rate from percentage to decimal:
- 14% as a decimal is 0.14 (since 14% = 14/100 = 0.14).
3. Simple Interest Formula:
- The formula for simple interest is:
[tex]\[
\text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time}
\][/tex]
- Rearrange this formula to solve for the principal (P):
[tex]\[
\text{Principal} = \frac{\text{Interest}}{\text{Rate} \times \text{Time}}
\][/tex]
4. Substitute the given values into the formula:
- Interest (I) = GH₵ 3500.00
- Rate (R) = 0.14
- Time (T) = 5 years
So we have:
[tex]\[
\text{Principal} = \frac{3500.00}{0.14 \times 5}
\][/tex]
5. Calculate the denominator:
- Multiply the rate by the time:
[tex]\[
0.14 \times 5 = 0.70
\][/tex]
6. Divide the interest by the result:
- Now, divide the interest by this product to find the principal:
[tex]\[
\text{Principal} = \frac{3500.00}{0.70} = 5000.00
\][/tex]
7. Conclusion:
- Therefore, the amount deposited by the man was GH₵ 5000.00
So, the man deposited an amount of GH₵ 5000.00 in his savings account.
