Question

B) Option 2 : Deposit regular monthly payments into an investment account. Formula given = A=Px [(1+r/12)^12t -1]/ (r/12)

1. John doesn't have enough to make a one time deposit, but he can make monthly payments into a retirement account. Suppose John makes $125 monthly payments into an account with a rate of return of 9.8%. How much would he have at age of 50? (Hit: John is 18 years old.)

2.    ii) If John were to increase his monthly deposit amount to $200, How old (to the nearest year) would John be when the balance reaches $1,000,000? (Hit: John is 18 years old.)

3. iii) What monthly deposit amount would be required for John to get $1,000,000 by age 50? (Hit: John is 18 years old.)

1. How much money would John actually have invested under these circumstances?
2. How much interest would have been earned in that time?

4. iv) What if John decided to wait until age 60 to retire?   In other words, if he made the same payments found in part iii above, how much would be in his account at that time? Is that total more than, less than, or equal to what you would expect? Give an explanation as to why you believe that is the case. (Hit: John is 18 years old.)

Note: please turn in all the exercises the following (step by step).

Option 3: Reflection: Write a short essay about what you discovered in this assignment. What are the primary strengths and challenges of each saving option? You can write it below or on separate paper.

Note: please turn in all the exercises the following (step by step).

Answer 1

i)i) Time = 50-18 = 32years = 32*12 = 384 months

Interest rate = 9.8% pa compounded monthly = 9.8%/12 monthly

Principal deposited each month = $125

Balance at age 50 = 125*(1/(9.8%/12))*((1+9.8%/12)^384 - 1) = $332455.4

(ii) Let it take t months for the balance to hit $1,000,000

$1,000,000 = 200*(1/(9.8%/12))*((1+9.8%/12)^t - 1)

Solving the above equation, we get t = 459 months = 38years+3months

Johns age = 18+38 = 56 years (nearest year)

(iii) Let the monthly deposit be P

P*(1/(9.8%/12))*((1+9.8%/12)^384 - 1) = $1,000,000

Solving the above equation, we get P = $376

(iv) retirement age = 60

time period = 60-18 = 42 years = 504 months

Monthly payment = $200

Balance in account = 376*(1/(9.8%/12))*((1+9.8%/12)^504 - 1) = $2,730,016

It is more than his expectation of $1,000,000 as the tenure for monthly annuity was increased by 120 months (or 10 years)