Edward Johnson decided to open up a Superannuation account.He will invest $1,800 per year for the next 35 years.Deposits to the Superannuation account will be made via a $150 payroll deduction at the end of each month.Assume that Edward will earn 8.75% annual interest compounded monthly over the life of his Super contribution.How much will he have at the end of 35 years?
A)$125,250
B)$250,321
C)$363,000
D)$414,405

Question

Quizplus · Accepted Answer

To solve this problem, we need to use the formula for the future value of an annuity due with monthly contributions:

FV = PMT * [(1 + r)^n - 1] / r * (1 + r)

Where:

PMT = $150 (monthly contributions)
r = 8.75% / 12 = 0.0072917 (monthly interest rate)
n = 35 years * 12 months/year = 420 (total number of months)

Plugging these values into the formula, we get:

FV = $150 * [(1 + 0.0072917)^420 - 1] / 0.0072917 * (1 + 0.0072917)
FV = $386,204.17

However, this formula only calculates the future value of the monthly contributions. To determine the total amount in the account at the end of 35 years, we need to add the initial deposit of $1,800 made at the beginning of each year for 35 years:

Total = FV + $1,800 * 35
Total = $386,204.17 + $63,000
Total = $449,204.17

Therefore, Edward will have $449,204.17 at the end of 35 years. The closest answer choice is D) $414,405, but this is not correct.

Edward Johnson Decided to Open Up a Superannuation Account