1. **Problem Statement:** Caleb contributes 2750 at the end of every 3 months (quarterly) for 5 years into an RRSP earning 2.50% interest compounded quarterly. We need to find: a. The future value of the fund at the end of 5 years. b. The amount of interest earned over the 5-year period. 2. **Formula Used:** The future value of an ordinary annuity compounded periodically is given by: $$FV = P \times \frac{(1 + r)^n - 1}{r}$$ where: - $P$ = payment amount per period - $r$ = interest rate per period - $n$ = total number of payments 3. **Given Data:** - $P = 2750$ - Annual interest rate = 2.50% = 0.025 - Compounded quarterly, so quarterly interest rate $r = \frac{0.025}{4} = 0.00625$ - Number of years = 5 - Number of quarters $n = 5 \times 4 = 20$ 4. **Calculate Future Value:** $$FV = 2750 \times \frac{(1 + 0.00625)^{20} - 1}{0.00625}$$ Calculate $(1 + 0.00625)^{20}$: $$1.00625^{20} \approx 1.131408$$ Then: $$FV = 2750 \times \frac{1.131408 - 1}{0.00625} = 2750 \times \frac{0.131408}{0.00625}$$ $$= 2750 \times 21.02528 = 57819.52$$ 5. **Calculate Interest Earned:** Total amount contributed: $$2750 \times 20 = 55000$$ Interest earned: $$57819.52 - 55000 = 2819.52$$ **Final Answers:** - a. Future value of the fund after 5 years is **57819.52** - b. Interest earned over 5 years is **2819.52**