Question

Devon is young and has just graduated college with her associate’s degree. She plans to start saving money for retirement as soon as she starts her new job. By taking 10% of her monthly gross income, Devon is able
to contribute (a) $__________ each month to a retirement plan. The account is expected to earn interest with an APR of 5.25% compounded monthly. Round answers to two decimal places.
a. How much money will be in Devon’s retirement account if she continues to make the same monthly
.
investment for 40 years?
b. Overall, Devon contributed how much of her own money into the retirement account?
c. What percent of the final balance in Devon’s retirement account was interest?

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Part 1: Continued
2. Later in life, Devon convinces her friend Taylor to start saving for retirement as well. Even though Taylor is the same age as Devon, she hasn’t started saving for retirement yet. With only 20 years left until they both plan to retire, Taylor decides she needs to invest at least twice as much as Devon each month to try to catch up to Devon’s retirement plan. Taylor opens a similar retirement account to Devon’s that also has an APR
5.25% compounded monthly. She will invest (b) $__________ per month. Round answers to two decimal places.
a. How much money will be in Taylor’s retirement account if she continues to make the same monthly
investment for 20 years?
b. By the time she retires, Taylor will have contributed how much of her own money overall?
c. What percent of the final balance in Taylor’s retirement account will be interest?
3. Write complete sentences that identify which person had the higher amount and by how much. Round answers to two decimal places.
a. Who had more money in their retirement account when they planned to retire? How much more?
b. Who contributed more to their retirement account? How much more?

Answer 1

Part 1: Devon is able to contribute (a) $450 each month to a retirement plan.

a. The amount in Devon's retirement account if she makes the same monthly investment for 40 years is $733,253.26.

b. Overall, Devon's total contribution of her own money into the retirement account is $216,000.

c. The percent of the final balance in Devon's retirement account that was interest was 70.5%.

Part 2: Taylor will invest (b) $1,733.00 per month.

a. The amount that will be in Taylor's retirement account if she makes the same monthly investment for 20 years is $733,253.26.

b. By the time that Taylor retires, she will have contributed $415,920 of her own money into the account.

c. The percent of the final balance in Taylor's retirement account that will be interest is 43.3%.

3. Both Devon and Taylor had the same amount, $733,253.26, in their retirement accounts when they planned to retire.

a. None had more money at their retirement.

b. Taylor contributed more to her retirement account by $199,920 ($414,920 - $216,000).

Data and Calculations:

Devon's Investments:

Gross monthly income = $4,500

APR = 5.25% compounded monthly

N (# of periods) = 480 months (12 x 40 years)

I/Y (Interest per year) = 5.25%

PV (Present Value) = $0

PMT (Periodic Payment) = $450 ($4,500 x 10%)

Results:

FV = $733,253.26 ($517,253.26 + $216,000)

Sum of all periodic payments = $216,000 ($450 x 480)

Total Interest = $517,253.26

Percentage of interest out of the FV = 70.5% ($517,253.26/$733,253.26 x 100)

Taylor's Investment:

N (# of periods) = 240 months (12 x 20 years)

I/Y (Interest per year) = 5.25%

PV (Present Value) = $0

FV (Future Value) = $733,253.26

Results:

PMT = $1,733.00

Sum of all periodic payments = $415,920 ($1,733 x 240

Total Interest = $317,333.26

Percentage of interest out of the FV = 43.3% ($317,333.26/$733,253.26 x 100)

Thus, based on the time value of money of investments, it is more profitable to start investing early.

Learn more about time value of money at https://brainly.com/question/15053018

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