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![**Problem 6**: Find the present value of a perpetuity with payments of ₱600 every 3 months, with an interest rate of 6% compounded quarterly.
*Explanation*:
A perpetuity is a financial instrument that provides endless periodic payments. To find its present value, use the formula for perpetuities. Given the periodic payments and the interest rate compounding frequency, the calculation requires adjusting the rate to align with the payment frequency.
**Details of the Calculation**:
- **Payment Amount**: ₱600 every 3 months
- **Nominal Annual Interest Rate**: 6%
- **Compounding Frequency**: Quarterly
**Steps**:
1. Adjust the annual nominal interest rate to reflect the quarterly compounding:
\[
\text{Quarterly Interest Rate} = \frac{6\%}{4} = 1.5\%
\]
2. The present value (PV) of a perpetuity is calculated using the formula:
\[
PV = \frac{\text{Payment Amount}}{\text{Effective Quarterly Interest Rate}}
\]
3. Substitute into the formula:
\[
PV = \frac{600}{0.015} = 40,000
\]
Thus, the present value of the perpetuity is ₱40,000.](https://content.bartleby.com/qna-images/question/7e6a052f-c3c0-401e-911e-0dc9c9983002/94db6d7b-f2de-4f03-bc26-507ec1b937e6/vq7luy_processed.jpeg)
Transcribed Image Text:**Problem 6**: Find the present value of a perpetuity with payments of ₱600 every 3 months, with an interest rate of 6% compounded quarterly.
*Explanation*:
A perpetuity is a financial instrument that provides endless periodic payments. To find its present value, use the formula for perpetuities. Given the periodic payments and the interest rate compounding frequency, the calculation requires adjusting the rate to align with the payment frequency.
**Details of the Calculation**:
- **Payment Amount**: ₱600 every 3 months
- **Nominal Annual Interest Rate**: 6%
- **Compounding Frequency**: Quarterly
**Steps**:
1. Adjust the annual nominal interest rate to reflect the quarterly compounding:
\[
\text{Quarterly Interest Rate} = \frac{6\%}{4} = 1.5\%
\]
2. The present value (PV) of a perpetuity is calculated using the formula:
\[
PV = \frac{\text{Payment Amount}}{\text{Effective Quarterly Interest Rate}}
\]
3. Substitute into the formula:
\[
PV = \frac{600}{0.015} = 40,000
\]
Thus, the present value of the perpetuity is ₱40,000.
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