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a. What will be the maturity value of [tex]\$15,000[/tex] placed in a 120-day term deposit paying an interest rate of [tex]2.25\%[/tex]? (Do not round intermediate calculations and round your final answer to 2 decimal places.)

Maturity value: [tex]\$\square[/tex]

b. If, on the maturity date, the combined principal and interest are "rolled over" into a 90-day term deposit paying [tex]2.15\%[/tex], what amount will the depositor receive when the second term deposit matures? (Do not round intermediate calculations and round your final answer to 2 decimal places.)

Maturity value: [tex]\$\square[/tex]

Sagot :

GinnyAnswer
Certainly! Let's solve each part step-by-step.

### Part (a)

To calculate the maturity value of a $15,000 term deposit for 120 days at an interest rate of 225%, we use the simple interest formula, which is:

[tex]\[ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \][/tex]

Where:
- \( \text{Principal} = \$15,000 \)
- \( \text{Rate} = 225\% = \frac{225}{100} = 2.25 \)
- \( \text{Time} = \frac{120 \text{ days}}{365 \text{ days/year}} \)

First, calculate the interest:
[tex]\[ \text{Interest} = 15,000 \times 2.25 \times \frac{120}{365} \][/tex]

Next, add the interest to the principal to find the maturity value:
[tex]\[ \text{Maturity Value (Part a)} = 15,000 + \text{Interest} \][/tex]

After evaluating the above expression, we get:
[tex]\[ \text{Maturity Value (Part a)} \approx \$26,095.89 \][/tex]

### Part (b)

For the second part, we take the maturity value from Part (a) and roll it over into a new term deposit. The new principal is the maturity value from Part (a), and we calculate the maturity value for 90 days at an interest rate of 2.15%.

Using the same formula:
[tex]\[ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \][/tex]

Where:
- \( \text{Principal} = \$26,095.89 \) (the maturity value from Part (a))
- \( \text{Rate} = 2.15\% = \frac{2.15}{100} = 0.0215 \)
- \( \text{Time} = \frac{90 \text{ days}}{365 \text{ days/year}} \)

First, calculate the interest for the second term:
[tex]\[ \text{Interest} = 26,095.89 \times 0.0215 \times \frac{90}{365} \][/tex]

Next, add the interest to the principal to find the new maturity value:
[tex]\[ \text{Maturity Value (Part b)} = 26,095.89 + \text{Interest} \][/tex]

After evaluating the above expression, we get:
[tex]\[ \text{Maturity Value (Part b)} \approx \$26,234.23 \][/tex]

### Summary

Therefore:

a. The maturity value for the $15,000 placed in a 120-day term deposit at 225% is:
[tex]\[ \$26,095.89 \][/tex]

b. The maturity value for the combined principal and interest rolled over into a 90-day term deposit at 2.15% is:
[tex]\[ \$26,234.23 \][/tex]
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