Asked by Neisha Bethly on Apr 27, 2024

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Martina's RRSP earns 12% compounded monthly and her goal is to accumulate $1,000,000 by making deposits of $4,100 at the end of every year. How many years will it take to reach her goal?

A) 24 years
B) 29 years
C) 33 years
D) 47 years
E) 125 years

Compounded Monthly

A method of calculating interest where the interest earned each month is added to the principal, thus earning interest in subsequent months.

RRSP

Registered Retirement Savings Plan, a Canadian account for holding savings and investment assets with tax benefits for retirement.

Deposits

Funds placed into an account at a financial institution for safekeeping or to earn interest.

  • Calculate the necessary regular contributions to reach a particular financial target within a specified period.
  • Examine multiple investment tactics to fulfill long-term financial aspirations.
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HM
Henriette MuharabuApr 29, 2024
Final Answer :
B
Explanation :
To solve this, we use the formula for the future value of a series of annuity payments compounded at a different frequency than the payments are made. The formula is: FV=P×((1+r/n)nt−1r/n)FV = P \times \left( \frac{(1 + r/n)^{nt} - 1}{r/n} \right)FV=P×(r/n(1+r/n)nt1) , where FVFVFV is the future value of the annuity, PPP is the payment amount, rrr is the annual interest rate, nnn is the number of compounding periods per year, and ttt is the time in years. In this case, P=$4,100P = \$4,100P=$4,100 , r=0.12r = 0.12r=0.12 , and n=12n = 12n=12 for monthly compounding. We solve for ttt when FV=$1,000,000FV = \$1,000,000FV=$1,000,000 . This requires iterative calculation or financial calculator/financial function in a spreadsheet, and the closest answer is 29 years.