Find the payment made by the ordinary annuity with the given present value.
​$92 comma 593​; monthly payments for 15 ​years; interest rate is 5.9​%, compounded monthly

To find the payment made by an ordinary annuity, we can use the formula for the present value of an ordinary annuity:

\[
PV = P \times \left[ \frac{1 - (1 + r)^{-n}}{r} \right]
\]

Where:
- $ PV $ is the present value (in this case, \$92,593),
- $ P $ is the payment (which we need to find),
- $ r $ is the monthly interest rate,
- $ n $ is the total number of payments.

### Step 1: Identify the known values
- Present Value $ PV = 92,593 $
- Interest rate $ 5.9\% $ annually, compounded monthly. To find the monthly interest rate, we divide the annual interest rate by 12:
  \[
  r = \frac{5.9\%}{12} = \frac{0.059}{12} = 0.00491667
  \]
- Duration: 15 years. The total number of payments $ n $ is the number of months in 15 years:
  \[
  n = 15 \times 12 = 180
  \]

### Step 2: Rearrange the formula to solve for $ P $ (the payment)
\[
P = \frac{PV \times r}{1 - (1 + r)^{-n}}
\]

Now we can plug in the known values and calculate the payment.

I'll compute that next.The monthly payment for the ordinary annuity is approximately **$776.36**.

Would you like more details on the calculation, or do you have any further questions?

Here are 5 related questions for deeper understanding:
1. How does the formula for future value differ from the present value of an annuity?
2. What happens to the monthly payment if the interest rate changes to 6%?
3. How would the payment change if the annuity duration was reduced to 10 years?
4. What is the total amount paid over the entire duration of the annuity?
5. Can you calculate the interest portion of each payment?

**Tip:** Increasing the number of periods in an annuity lowers the payment, even at the same interest rate.

Find the payment made by the ordinary annuity with the given present value: $92,593; monthly payments for 15 years; interest rate is 5.9%, compounded monthly.

Learn how to calculate the monthly payment for an ordinary annuity with a present value of $92,593, 5.9% interest compounded monthly, and a 15-year term. This detailed solution involves the use of the annuity formula and compound interest calculations.

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