Questions: Find the future value for the ordinary annuity with the given payment and interest rate. PMT = 2,000; 1.70% compounded monthly for 6 years. The future value of the ordinary annuity is . (Do not round until the final answer. Then round to the nearest cent as needed.)

Find the future value for the ordinary annuity with the given payment and interest rate.

PMT = 2,000; 1.70% compounded monthly for 6 years.

The future value of the ordinary annuity is . (Do not round until the final answer. Then round to the nearest cent as needed.)

Transcript text: Find the future value for the ordinary annuity with the given payment and interest rate. PMT $=\$ 2,000 ; 1.70 \%$ compounded monthly for 6 years. The future value of the ordinary annuity is $\$$ $\square$ . (Do not round until the final answer. Then round to the nearest cent as needed.)

Solution

Solution Steps

Step 1: Identify the Parameters

The periodic payment amount (PMT) is 2000, the annual interest rate (r) is 0.017, the number of compounding periods per year (n) is 12, and the total number of years (t) is 6.

Step 2: Apply the Future Value of an Ordinary Annuity Formula

The formula to calculate the future value (FV) of an ordinary annuity is: $$ FV = PMT \times \left( \frac{(1 + \frac{r}{n})^{n \times t} - 1}{\frac{r}{n}} \right) $$

Step 3: Substitute the Parameters into the Formula

Substituting the given values into the formula, we get: $$ FV = {PMT} \times \left( \frac{{(1 + \frac{{{r}}}{{{n}}})^{{{n}} \times {t}}} - 1}{{\frac{{{r}}}{{{n}}}}} \right) $$

Step 4: Calculate the Future Value

After performing the calculations, the future value of the annuity is approximately 151487.35.