Priya and Leo each invest $2500 for 6 years. By calculating the interest earned over the 6 years, determine who will have the greater amount. (3 marks) --- 10 WORK AREA LINES (style=lined) ---
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Priya and Leo each invest $2500 for 6 years. By calculating the interest earned over the 6 years, determine who will have the greater amount. (3 marks) --- 10 WORK AREA LINES (style=lined) --- \(\text{Priya’s investment:}\) \(\text{Interest} = Prn = 2500 \times 0.058 \times 6 = \$870\) \(\text{Leo’s investment:}\) \(r = \dfrac{4.5\%}{2} = 2.25\% \text{ per half-year}\) \(\text{Compounding periods} = 6 \times 2 = 12\) \(FV = PV(1+r)^n = 2500(1+0.0225)^{12} = \$3211.83\) \(\text{Total interest} = FV-PV = 3211.83-2500 = \$711.83\) \(\text{Priya’s interest } > \text{ Leo’s interest.}\) \(\Rightarrow \text{Priya will have a greater amount (since original investment the same)}\) \(\text{Priya’s investment:}\) \(\text{Interest} = Prn = 2500 \times 0.058 \times 6 = \$870\) \(\text{Leo’s investment:}\) \(r = \dfrac{4.5\%}{2} = 2.25\% \text{ per half-year}\) \(\text{Compounding periods} = 6 \times 2 = 12\) \(FV = PV(1+r)^n = 2500(1+0.0225)^{12} = \$3211.83\) \(\text{Total interest} = FV-PV = 3211.83-2500 = \$711.83\) \(\text{Priya’s interest } > \text{ Leo’s interest.}\) \(\Rightarrow \text{Priya will have a greater amount (since original investment the same)}\)
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