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To find the present value (PV) or purchase price of the annuity, we need to compute the PV of both payment streams separately:

1. **First Stream ($700 per quarter for 3 years)**: 
   - Payment occurs at the beginning of each quarter.
   - This forms an annuity due with quarterly payments of $700 for 3 years, which is 12 quarters.

2. **Second Stream ($400 per quarter for the next 2 years)**:
   - This is also an annuity due with quarterly payments of $400 for 2 years, which is 8 quarters.

### Steps:
1. Convert the semi-annual interest rate to a quarterly effective rate.
2. Calculate the PV of the first annuity due (for 3 years at $700 per quarter).
3. Calculate the PV of the second annuity due (for 2 years at $400 per quarter).
4. Discount the second annuity to account for the fact that it starts 3 years later.

Would you like a detailed calculation for each step? 

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Here are related questions to explore:
1. How is the annuity due different from an ordinary annuity?
2. How does changing the compounding period affect the present value?
3. What happens to the PV if the interest rate increases?
4. Can this annuity calculation be adjusted for monthly payments?
5. How would deferred payments affect the calculation?

**Tip**: When calculating annuities, always ensure you understand the compounding frequency and payment frequency to avoid mistakes.

An annuity provides $700 beginning-of-quarter payments for the first three years and $400 beginning-of-quarter payments for the next two years. What is the purchase price of the annuity if the interest rate is 3.7% compounded semi-annually?

Find the purchase price of an annuity with $700 quarterly payments for three years and $400 for two years, compounded at 3.7% semi-annually. This finance problem covers annuity due and present value calculations.

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