Question 6 Find the equivalent future value at year 7 of an annuity from year 4 to year 6 with an annuity amount of $200 per year at an annual rate of 10%? O O 812 728 746 781
Question 6 Find the equivalent future value at year 7 of an annuity from year 4 to year 6 with an annuity amount of $200 per year at an annual rate of 10%? O O 812 728 746 781
Chapter1: Making Economics Decisions
Section: Chapter Questions
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![**Question 6**
Find the equivalent future value at year 7 of an annuity from year 4 to year 6 with an annuity amount of $200 per year at an annual rate of 10%.
- 812
- 728
- 746
- 781
**Explanation:**
This question involves calculating the future value of an annuity. The annuity is paid for three years (year 4 to year 6), and we need to find out what its value will be in year 7 given a 10% annual interest rate.
To find the future value of each annuity payment, you apply the future value formula for each year and sum the results:
1. **Year 4 Payment:** Calculate the future value in year 7
\[
FV = 200 \times (1 + 0.10)^{3}
\]
2. **Year 5 Payment:** Calculate the future value in year 7
\[
FV = 200 \times (1 + 0.10)^{2}
\]
3. **Year 6 Payment:** Calculate the future value in year 7
\[
FV = 200 \times (1 + 0.10)^{1}
\]
Add these future values to find the total future value of the annuity at year 7.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0655393b-8df3-4633-b13c-e0d6983d2306%2Ff68ec616-5225-4377-ad96-abee12ecd6fd%2F6tqoxh_processed.png&w=3840&q=75)
Transcribed Image Text:**Question 6**
Find the equivalent future value at year 7 of an annuity from year 4 to year 6 with an annuity amount of $200 per year at an annual rate of 10%.
- 812
- 728
- 746
- 781
**Explanation:**
This question involves calculating the future value of an annuity. The annuity is paid for three years (year 4 to year 6), and we need to find out what its value will be in year 7 given a 10% annual interest rate.
To find the future value of each annuity payment, you apply the future value formula for each year and sum the results:
1. **Year 4 Payment:** Calculate the future value in year 7
\[
FV = 200 \times (1 + 0.10)^{3}
\]
2. **Year 5 Payment:** Calculate the future value in year 7
\[
FV = 200 \times (1 + 0.10)^{2}
\]
3. **Year 6 Payment:** Calculate the future value in year 7
\[
FV = 200 \times (1 + 0.10)^{1}
\]
Add these future values to find the total future value of the annuity at year 7.
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