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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.

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