1. **Problem Statement:** Mr. Tomas contributes 202 at the end of each month into an RRSP with an interest rate of 3% per annum compounded quarterly. We want to find the total amount after 10 years and the interest earned. 2. **Formula Used:** For regular contributions with compound interest, the future value of an annuity formula is used: $$ A = P \times \frac{(1 + r/n)^{nt} - 1}{(r/n)} $$ where: - $A$ is the amount accumulated after $t$ years, - $P$ is the payment per period, - $r$ is the annual interest rate (decimal), - $n$ is the number of compounding periods per year, - $t$ is the number of years. 3. **Important Notes:** - Contributions are monthly, but compounding is quarterly. - We must adjust the formula to account for monthly payments and quarterly compounding. - The effective interest rate per month is calculated from the quarterly rate. 4. **Calculations:** - Annual interest rate $r = 0.03$ - Quarterly compounding periods per year $n = 4$ - Total years $t = 10$ - Total months $m = 10 \times 12 = 120$ 5. **Calculate quarterly interest rate:** $$ i_q = \frac{r}{n} = \frac{0.03}{4} = 0.0075 $$ 6. **Calculate effective monthly interest rate:** Since compounding is quarterly, the monthly interest rate $i_m$ is: $$ i_m = (1 + i_q)^{1/3} - 1 = (1 + 0.0075)^{\frac{1}{3}} - 1 $$ Calculate: $$ i_m = 1.0075^{0.333333} - 1 \approx 0.002495 $$ 7. **Apply future value of annuity formula with monthly payments and monthly interest rate:** $$ A = P \times \frac{(1 + i_m)^m - 1}{i_m} $$ Substitute values: $$ A = 202 \times \frac{(1 + 0.002495)^{120} - 1}{0.002495} $$ Calculate: $$ (1 + 0.002495)^{120} = 1.349353 $$ So: $$ A = 202 \times \frac{1.349353 - 1}{0.002495} = 202 \times \frac{0.349353}{0.002495} $$ Calculate fraction: $$ \frac{0.349353}{0.002495} = 139.995991 $$ Multiply: $$ A = 202 \times 139.995991 = 28279.119982 $$ Rounded to nearest cent: $$ A = 28279.12 $$ 8. **Calculate total contributions:** $$ \text{Total contributions} = 202 \times 120 = 24240 $$ 9. **Calculate interest earned:** $$ \text{Interest} = A - \text{Total contributions} = 28279.12 - 24240 = 4039.12 $$ **Final answers:** - Total amount after 10 years: **28279.12** - Interest earned: **4039.12**