Can someone please help me on this one ?

You are considering different investment strategies to save for your retirement.
Option 1: You invest $50/ month at a rate of 3.5% APR compounded monthly for 35 years.
Option 2: You invest $150/ quarter at a rate of 4.15% APR compounded monthly for 35 years.
Option 3: You invest $4,000 at a rate of 5.5% APR compounded monthly for 35 years.
Complete the table below and answer the questions below it.
You may use this calculator http://www.mycalculators.com/ca/savecalcm.html to help you.
(Hint: The “Present Value” for options 1 and 2 is 0 while for option 3 it is $4,000.00. Also, the
top radio button in the Contributions box should be selected so that contributions are made at the beginning of the period.)

Table:
Option # | Contributions | Final Balance | Total Interest Earned
1
2
3

1) How did you calculate the contribution for each option? In which option would you
contribute the least?

2) Which option yielded the highest amount at the end of the 35 years and what was the basis of the plan?

3) What is the difference in the principal invested for the highest and lowest final
balances? What is the difference in the interest earned?

4) What plan would you recommend for the largest return on investment? (This means
the most interest for the least amount invested)

5) How does the differing interest rates in each option play into your recommendation?

I would appreciate full feedback! Thank you :)

Question

timothydrake timothydrake

23-11-2021
Mathematics

contestada

Can someone please help me on this one ?

You are considering different investment strategies to save for your retirement.
Option 1: You invest $50/ month at a rate of 3.5% APR compounded monthly for 35 years.
Option 2: You invest $150/ quarter at a rate of 4.15% APR compounded monthly for 35 years.
Option 3: You invest $4,000 at a rate of 5.5% APR compounded monthly for 35 years.
Complete the table below and answer the questions below it.
You may use this calculator http://www.mycalculators.com/ca/savecalcm.html to help you.
(Hint: The “Present Value” for options 1 and 2 is 0 while for option 3 it is $4,000.00. Also, the
top radio button in the Contributions box should be selected so that contributions are made at the beginning of the period.)

Table:
Option # | Contributions | Final Balance | Total Interest Earned
1
2
3

1) How did you calculate the contribution for each option? In which option would you
contribute the least?

2) Which option yielded the highest amount at the end of the 35 years and what was the basis of the plan?

3) What is the difference in the principal invested for the highest and lowest final
balances? What is the difference in the interest earned?

4) What plan would you recommend for the largest return on investment? (This means
the most interest for the least amount invested)

5) How does the differing interest rates in each option play into your recommendation?

I would appreciate full feedback! Thank you :)

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oeerivona oeerivona · Answer 1 · 2021-12-04T08:12:47+01:00

Return on investment increases as the interest rate applied, the duration of investment, and the principal invested increases.

The responses are as follows;

1) Total contribution = Single contribution Value × Number of contributions

2) Option 2

3) $-4,000

4) Option 3

5) The higher interest rate increases the return on investment

Reasons:

Option 1: Investment

The present value = 0

The contributions made = $50 monthly

APR of investment = 3.5%

Number of years of investment = 35 years

The contribution = $50 × 12 × 35 = $21,000

Future value (final balance) = $41,230.22

Interest Earned = $41,230.22 - $21,000 = $20,230.22

Option 2: Investment

The present value = 0

The contributions made = $150 per quarter

APR on investment = 4.15%

Number of years of investment = 35 years

The contribution = $150 × 4 × 35 = $21,000

Future value = $47,503.88

Interest Earned = $47,503.88 - $21,100

Option 3: Investment

Present value = $4,000

APR on investment = 5.5%

Number of years of investment = 35 years

The contribution = $4,000

Future value = $27,300.26

Interest Earned = $27,300.26 - $4,000 = $23,300.26

[tex]\begin{array}{|c|c|c|c|}Option \ number&Contributions&Total \ Interest \ Earned&Final \ Balance\\1&\$50&\$20,230.22&\$41,230.22\\2&\$150&\$26,403.88&\$47,503.88\\3& \$4,000 &\$23,300.26 &\$27,300.26 \end{array}\right][/tex]

1) The total contribution is given by the product of the monthly contribution and the number of timer units.

2) The option that yielded the highest amount at the end of 35 years is the option 2.

The basis of the plan is quarterly investment of $150 and an annual interest rate of 4.15% compounded monthly.

3) The principal with the highest final balance is the principal for Option 2. which is 0

The principal that has the lowest final balance is the principal for option 3 which is $4,000

The difference in the principal for the highest and lowest final balances is

$0 - $4,000 = $-4,000

4) The plan recommended for the largest return on investment is option 2, in which the amount invested increased by more than 600%

5) The higher the interest rate, the higher the return on the amount invested.

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