2) Virat landed his first job at Telus upon graduating from Concordia in December 2023. After his 3 months of probation, Virat was offered to participate in Telus’ Group Registered Retirement Savings Plan (RRSP). As he is only 22 years old, he is not yet ready to think about retirement and therefore decided not to participate in the company offering, even if the company would have matched his $300 monthly contribution. Assume that Virat would retire at age 65, how much would he have accumulated in his retirement plan if the plan averaged an annual return of 7% interest compounded semi-monthly?
a) $1,839,331
b) $1,749,563
c) $2,105,010
d) $1,667,227
e) $1,971,849
To calculate Virat's retirement savings accumulation, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/retirement savings
P = the principal contribution (monthly contribution)
r = annual interest rate (7% or 0.07)
n = number of times the interest is compounded per year (semi-monthly means 24 times a year)
t = number of years (65 years - 22 years = 43 years)
First, calculate the monthly contribution that would have been matched by the company:
$300 x 2 (company matching) = $600
Now, calculate the future value of the investment:
A = $600(1 + 0.07/24)^(24*43)
A = $600(1 + 0.00291666667)^(1032)
A = $600(1.00291666667)^1032
A = $600(6.81493)
A = $4,088.96
Given that Virat didn't participate in the company plan, he would only have his own contributions:
$300 x 43 x 12 = $154,800
Therefore, the total amount accumulated in his retirement plan would be:
$4,088.96 + $154,800 = $158,888.96
The closest option is d) $1,667,227. This might be a mistake in the question or the options given.