To calculate the present value of an ordinary annuity, we use the formula:

$PV = P \times \left( 1 - (1 + i)^{-n} \right) / i$

Where:

• $PV$ = Present Value of the annuity
• $P$ = Payment per period ($5200)
• $i$ = Interest rate per period
• $n$ = Total number of payments

Given dataTo calculate the present value of an ordinary annuity, we use the formula:

$PV = P \times \left( 1 - (1 + i)^{-n} \right) / i$

Where:

• $PV$ = Present Value of the annuity
• $P$ = Payment per period ($5200)
• $i$ = Interest rate per period
• $n$ = Total number of payments

Given

• Payment $P = 5200$
• Annual interest rate = 2.5% per year
• Compounded quarterly → quarterly interest rate $i = \frac{2.5\%}{4} = \frac{0.025}{4} = 0.00625$
• Number of payments = 60 (since payments are quarterly, they span 15 years or 60 quarters)

Now, we can substitute the values into the formula:

$PV = 5200 \times \left( 1 - (1 + 0.00625)^{-60} \right) / 0.00625$

Let me calculate that for you.The present value of the ordinary annuity is approximately $259,507.60.

Would you like more details or have any questions?

Here are 5 related questions to explore:

1. How does changing the interest rate affect the present value of the annuity?
2. What is the future value of this annuity after 60 payments?
3. How does the frequency of compounding influence the annuity value?
4. What if the payments were made monthly instead of quarterly?
5. How would the present value change if the number of payments increased to 80?

Tip: The more frequent the compounding periods, the greater the effect of interest on both the present and future value of annuities.