Suppose you can afford $14,820 per year to invest into a savings annuity. Write
ID: 3198128 • Letter: S
Question
Suppose you can afford $14,820 per year to invest into a savings annuity. Write this value down, as you'll be using it throughout this entire problem. We are going to explore various options and how these options will impact the interest you are making.
Payment Frequency
Monthly
If you deposit your available money on a monthly basis, how much are you depositing per month? $
If you are earning 6.8% annual interest, what is the total value of the annuity at the end of 30 years? $
How much interest is earned at the end of 30 years? $
Weekly
If you deposit your available money on a weekly basis, how much are you depositing per week (52 weeks per year)? $
If you are earning 6.8% annual interest, what is the total value of the annuity at the end of 30 years? $
How much interest is earned at the end of 30 years? $
Rate
r = 6.8%
If you are making monthly deposits from your available funds, what is the total value in your annuity at the end of 30 years, given the rate is 6.8%? $
How much interest did you earn? $
r = 7.3%
If you are making monthly deposits from your available funds, what is the total value in your annuity at the end of 30 years, given the rate is 7.3%? $
How much interest did you earn? $
r = 7.8%
If you are making monthly deposits from your available funds, what is the total value in your annuity at the end of 30 years, given the rate is 7.8%? $
How much interest did you earn? $
Time
25 years
If you make monthly deposits at an annual rate of 6.8%, what is the total value in the account after 25 years? $
How much interest did you earn? $
30 years
If you make monthly deposits at an annual rate of 6.8%, what is the total value in the account after 30 years? $
How much interest did you earn? $
35 years
If you make monthly deposits at an annual rate of 6.8%, what is the total value in the account after 35 years? $
How much interest did you earn? $
40 years
If you make monthly deposits at an annual rate of 6.8%, what is the total value in the account after 40 years? $
How much interest did you earn? $
Conclusion
Which factor had the greatest impact on the amount of interest that you earned? Payment frequency, Rate, or Time
Explanation / Answer
Suppose you can afford $14,820 per year to invest into a savings annuity. Write this value down, as you'll be using it throughout this entire problem. We are going to explore various options and how these options will impact the interest you are making.
Payment Frequency
Monthly
If you deposit your available money on a monthly basis, how much are you depositing per month?
Answer :
Here Per month deposit = 14820/12 = $1235 per month
Total depoist in 30 years = 1235 * 12 * 30 = $ 444600
If you are earning 6.8% annual interest, what is the total value of the annuity at the end of 30 years?
Answer : FV= PMT * [(1 + i)n -1]/i
FV = 1235 * [(1 + 0.068/12)360 - 1] /(0.068/12)
FV = $ 1448535.56
How much interest is earned at the end of 30 years?
Interest earned = $ 1448535.56 - $ 444600 = $ 1003935.56
Weekly
If you deposit your available money on a weekly basis, how much are you depositing per week (52 weeks per year)? $
Here weekly deposit = 14820/52 = $ 285
If you are earning 6.8% annual interest, what is the total value of the annuity at the end of 30 years? $
FV= PMT * [(1 + i)n -1]/i
FV = 285 * [(1 + 0.068/52)1560 - 1] /(0.068/52)
FV = $ 1455927.01
How much interest is earned at the end of 30 years?
Interest earned = $ 1455927.01 - $ 444600 = $ 1011327.01
Rate
r = 6.8%
If you are making monthly deposits from your available funds, what is the total value in your annuity at the end of 30 years, given the rate is 6.8%? $
FV= PMT * [(1 + i)n -1]/i
FV = 1235 * [(1 + 0.068/12)360 - 1] /(0.068/12)
FV = $ 1448535.56
How much interest did you earn?
Interest earned = $ 1448535.56 - $ 444600 = $ 1003935.56
r = 7.3%
If you are making monthly deposits from your available funds, what is the total value in your annuity at the end of 30 years, given the rate is 7.3%?
FV= PMT * [(1 + i)n -1]/i
FV = 1235 * [(1 + 0.073/12)30 - 1] /(0.073/12)
FV = $ 1598962.27
How much interest did you earn? $
Interest earned = $ 1598962.27 - $ 444600 = $ 1154362.27
r = 7.8%
If you are making monthly deposits from your available funds, what is the total value in your annuity at the end of 30 years, given the rate is 7.8%? $
FV= PMT * [(1 + i)n -1]/i
FV = 1235 * [(1 + 0.078/12)30 - 1] /(0.078/12)
FV = $ 1767555.67
How much interest did you earn?
Interest earned = $ 1767555.67- $ 444600 = $ 1322955.67
Time
25 years
If you make monthly deposits at an annual rate of 6.8%, what is the total value in the account after 25 years?
FV= PMT * [(1 + i)n -1]/i
FV = 1235 * [(1 + 0.068/300)300- 1] /(0.068/300)
FV = $ 969346.41
How much interest did you earn? $
Interest earned = $ 969346.41- $ 444600 = $ 524746.41
30 years
If you make monthly deposits at an annual rate of 6.8%, what is the total value in the account after 30 years? $
FV= PMT * [(1 + i)n -1]/i
FV = 1235 * [(1 + 0.068/12)360 - 1] /(0.068/12)
FV = $ 1448535.56
How much interest did you earn? $
Interest earned = $ 1448535.56- $ 444600 = $ 1003935.56
35 years
If you make monthly deposits at an annual rate of 6.8%, what is the total value in the account after 35 years? $
FV= PMT * [(1 + i)n -1]/i
FV = 1235 * [(1 + 0.068/12)360 - 1] /(0.068/12)
FV = $ 2121135.39
How much interest did you earn?
Interest earned = $ 2121135.39- $ 444600 = $ 1676525.39
40 years
If you make monthly deposits at an annual rate of 6.8%, what is the total value in the account after 40 years? $
FV= PMT * [(1 + i)n -1]/i
FV = 1235 * [(1 + 0.068/12)360 - 1] /(0.068/12)
FV = $ 3065172.42
How much interest did you earn? $
Interest earned = $3065172.42- $ 444600 = $ 2620572.42
Conclusion
Which factor had the greatest impact on the amount of interest that you earned? Payment frequency, Rate, or Time
Here time is the most important factor here.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.