$1$ . Mr. Kumar has contributed $\$1825.00$ per year for the last eight years into RRSP accounts earning $6.4\%$ compounded semi-annually. a) How much will Kumar have in total in his RRSP accounts? b) How much did the Kumar's contribute? c) How much will be interest?

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Percent of change: word problems

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1

. Mr. Kumar has contributed

\$1825.00

per year for the last eight years into RRSP accounts earning

6.4\%

compounded semi-annually. a) How much will Kumar have in total in his RRSP accounts? b) How much did the Kumar's contribute? c) How much will be interest?

Calculate Future Value: Calculate the future value of an annuity due to regular contributions using the formula for future value of an annuity compounded semi-annually: $FV = P \times \left[(1 + r/n)^{(nt)} - 1\right] / (r/n)$ , where $P$ is the payment, $r$ is the annual interest rate, $n$ is the number of times the interest is compounded per year, and $t$ is the time in years.
Plug in Values: Plug in the values: $P = \$1825$ , $r = 6.4\%$ or $0.064$ , $n = 2$ (since it's compounded semi-annually), and $t = 8$ years.
Perform Calculations: Calculate the future value: $FV = 1825 \times \left[(1 + \frac{0.064}{2})^{(2\times8)} - 1\right] / \left(\frac{0.064}{2}\right)$ .
Calculate Value Inside Brackets: Perform the calculations: $FV = 1825 \times [(1 + 0.032)^{16} - 1] / 0.032$ .
Perform Exponentiation: Calculate the value inside the brackets: $(1 + 0.032)^{16} - 1$ .
Complete Calculation: Perform the exponentiation: $(1.032)^{16} - 1 \approx 1.747 - 1 \approx 0.747$ .
Perform Division and Multiplication: Complete the calculation for the future value: $FV = 1825 \times 0.747 / 0.032$ .
Calculate Future Value: Perform the division and multiplication: $FV \approx 1825 \times 23.34375$ .
Answer Part b: Calculate the future value: $FV \approx 1825 \times 23.34375 \approx (\$42627.34)$ .
Perform Multiplication: Answer part b) by calculating the total contributions: Total contributions = $P \times t = (\$1825) \times 8$ .
Answer Part c: Perform the multiplication for total contributions: Total contributions = $\$1825 \times 8 = \$14600$ .
Subtract Total Contributions: Answer part c) by calculating the interest earned: Interest = $FV - \text{Total contributions}.$
Perform Subtraction: Subtract the total contributions from the future value to find the interest: $\text{Interest} = \$42627.34 - \$14600.$
Perform Subtraction: Subtract the total contributions from the future value to find the interest: Interest = $\$42627.34 - \$14600$ . Perform the subtraction to find the interest: Interest $\approx \$42627.34 - \$14600 \approx \$28027.34$ .