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To solve the problem using the **amortization formula** or the **present value of an ordinary annuity formula**, we use the following formula for the present value of an ordinary annuity:

\[
PV = PMT \times \frac{1 - (1 + i)^{-n}}{i}
\]

Where:
- $ PV = 13,000 $ (Present Value)
- $ i = 0.02 $ (interest rate per period)
- $ PMT = 600 $ (payment per period)
- $ n = ? $ (number of periods)

We need to solve for $ n $. Rearranging the equation for $ n $:

\[
\frac{PV \times i}{PMT} = 1 - (1 + i)^{-n}
\]

Simplifying:

\[
\frac{13,000 \times 0.02}{600} = 1 - (1 + 0.02)^{-n}
\]

This becomes:

\[
0.4333 = 1 - (1.02)^{-n}
\]

Now solving for $ n $, I will proceed with the calculation.The calculated value of $ n $ is approximately 28.68. Since the problem asks to round up to the nearest integer, the number of periods $ n $ is:

\[
n = 29
\]

Would you like any additional details or clarification?

Here are 5 related questions to expand on this topic:
1. How is the present value of an annuity calculated in different scenarios?
2. What are the key differences between an ordinary annuity and an annuity due?
3. How does changing the interest rate affect the number of periods?
4. Can this formula be applied to continuous payments? If not, what adjustments are needed?
5. What are some real-life examples of where this type of calculation is used?

**Tip:** Always ensure your interest rate is consistent with the payment period (e.g., monthly rate for monthly payments).

Use the formula for the present value of an ordinary annuity or the amortization formula to solve the following problem. PV = $13,000; i = 0.02; PMT = $600; n = ?

Learn how to find the number of periods (n) in a present value annuity problem. Given PV = $13,000, interest rate i = 0.02, and periodic payment PMT = $600, we use the formula PV = PMT * (1 - (1 + i)^-n) / i to solve for n. Suitable for students in Grades 10-12 or college-level finance.

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