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You would like to save $ X00 (choose the amount) every month for the next 4 years. If the interest rate is 2% compounded quarterly, what would the accumulated value of your investment be at the end of 4 years?

Peter makes contributions of $500 at the beginning of every 6 months for X years (choose the time) towards an RRSP. If the RRSP earns interest at 5% compounded semi-annually, what would be the value of his RRSP at the end of the time period?

User Reason
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Final answer:

To find the accumulated value of saving $300 monthly at a 2% compounded quarterly rate after 4 years or the RRSP value after X years with $500 semi-annual contributions at 5% compounded semi-annually, you would use the formula for the future value of an annuity for ordinary (end-of-period) and annuity due (beginning-of-period) payments.

Step-by-step explanation:

If you wish to save $300 every month for the next 4 years with a 2% interest rate compound quarterly, the accumulated value can be calculated using the future value of an annuity formula. Assuming the contribution is made at the end of the period, and with n representing the total number of contributions, r the quarterly interest rate, and PV the monthly payment, the formula is FV = PV * [(1 + r)^n - 1] / r.

For Peter’s contributions to an RRSP, if he deposits $500 at the beginning of every 6 months for X years with an interest rate of 5% compounded semi-annually, we use the future value of an annuity due formula, considering the advance contributions. The future value of an annuity due is FV = PV * [(1 + r)^n - 1] / r * (1 + r), where contributions are made at the start of each period.

To calculate the exact figures, you would substitute the given values into these formulas. Remember that the quarterly interest rate is the annual rate divided by 4, and the semi-annual rate is the annual rate divided by 2. The most important point here is the effect of compound interest over time, as even small rates can lead to significant growth due to the frequency of compounding.

User Vrushank
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