Solve the following problem.

n equals 33n=33​; 

*i*equals 0.049=0.049​; 

PMT equals $ 188PMT=$188​; 

PV equals question markPV=?

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Part 1

PV equals $PV=$enter your response here 

​(Round to two decimal​ places.)

To find the present value (PV) of an annuity given the number of periods $ n = 33 $, the interest rate $ i = 0.049 $, and the payment amount $ PMT = \$188 $, we can use the present value formula for an annuity:

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

Let's calculate it step by step:

1. Given:
   \[ n = 33 \]
   \[ i = 0.049 \]
   \[ PMT = \$188 \]

2. Calculate $(1 + i)^{-n}$:
   \[ (1 + 0.049)^{-33} \]

First, calculate $1 + i$:
\[ 1 + 0.049 = 1.049 \]

Next, raise $1.049$ to the power of $-33$:
\[ 1.049^{-33} \approx 0.2281 \]

3. Calculate $1 - (1 + i)^{-n}$:
\[ 1 - 0.2281 = 0.7719 \]

4. Finally, calculate the present value:
\[ PV = 188 \times \frac{0.7719}{0.049} \approx 188 \times 15.7551 \approx 2962.95 \]

Therefore, the present value (PV) is approximately:

\[ \boxed{2962.95} \]

Would you like more details or have any questions?

### Related Questions

1. How does the present value of an annuity change if the interest rate increases?
2. What is the difference between the present value of an annuity and the future value of an annuity?
3. How do you calculate the present value of an annuity with varying payments?
4. What is the impact of the number of periods on the present value of an annuity?
5. How can you use the present value of an annuity formula to plan for retirement?
6. What is the present value of a perpetuity and how is it calculated?
7. How does changing the compounding frequency affect the present value of an annuity?
8. What factors should be considered when choosing an annuity investment?

### Tip

When calculating the present value of an annuity, ensure that the interest rate and the number of periods are consistent with the payment frequency (e.g., annual, semi-annual, quarterly).

Learn how to calculate the present value (PV) of an annuity with $188 payment per period, given an interest rate of 4.9% over 33 periods. Get a detailed step-by-step solution with formulas and calculations.

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