1. **Problem Statement:** We need to compare the growth of an investment of 1 unit at an annual interest rate of 10% for 0, 5, 10, 15, and 20 years. There are two cases: (a) Simple Interest (b) Compound Interest (compounded annually) 2. **Formulas:** - Simple Interest (SI): $$ A = P(1 + rt) $$ where $P$ is the principal, $r$ is the annual interest rate (in decimal), and $t$ is time in years. - Compound Interest (CI): $$ A = P(1 + r)^t $$ where $P$, $r$, and $t$ are as above. 3. **Given:** $P = 1$, $r = 0.10$, and $t = 0, 5, 10, 15, 20$ 4. **Calculations:** **(a) Simple Interest:** - For $t=0$: $$ A = 1(1 + 0.10 \times 0) = 1 $$ - For $t=5$: $$ A = 1(1 + 0.10 \times 5) = 1(1 + 0.5) = 1.5 $$ - For $t=10$: $$ A = 1(1 + 0.10 \times 10) = 1(1 + 1) = 2 $$ - For $t=15$: $$ A = 1(1 + 0.10 \times 15) = 1(1 + 1.5) = 2.5 $$ - For $t=20$: $$ A = 1(1 + 0.10 \times 20) = 1(1 + 2) = 3 $$ **(b) Compound Interest:** - For $t=0$: $$ A = 1(1 + 0.10)^0 = 1 $$ - For $t=5$: $$ A = 1(1.10)^5 = 1.61051 $$ - For $t=10$: $$ A = 1(1.10)^{10} = 2.59374 $$ - For $t=15$: $$ A = 1(1.10)^{15} = 4.17725 $$ - For $t=20$: $$ A = 1(1.10)^{20} = 6.72750 $$ 5. **Table of Values:** | Years | Simple Interest | Compound Interest | |-------|-----------------|-------------------| | 0 | 1.00 | 1.00 | | 5 | 1.50 | 1.61 | | 10 | 2.00 | 2.59 | | 15 | 2.50 | 4.18 | | 20 | 3.00 | 6.73 | **Conclusion:** Compound interest grows faster than simple interest over time due to interest on interest effect.