1. Calculate Simple Interest (SI) on 5,000 for 3 years at 6% p.a. SI formula: $$SI = \frac{P \times R \times T}{100}$$ Given: $$P = 5000, R = 6, T = 3$$ Calculate: $$SI = \frac{5000 \times 6 \times 3}{100} = 900$$ 2. Find Compound Interest (CI) on 8,000 for 2 years at 5% compounded annually. CI formula: $$A = P\left(1 + \frac{R}{100}\right)^T$$ CI = Amount - Principal Given: $$P = 8000, R = 5, T = 2$$ Calculate Amount: $$A = 8000 \times \left(1 + \frac{5}{100}\right)^2 = 8000 \times 1.1025 = 8820$$ CI: $$CI = 8820 - 8000 = 820$$ 3. A bill of 60,000 is discounted at 6% p.a. for 3 months before maturity. Find discount. Discount formula: $$D = \frac{P \times R \times T}{100}$$ Convert time to years: $$T = \frac{3}{12} = 0.25$$ Calculate: $$D = \frac{60000 \times 6 \times 0.25}{100} = 900$$ 4. Find present value of 10,000 due in 4 years at 7% p.a. SI. Present Value formula: $$PV = \frac{FV}{1 + \frac{R \times T}{100}}$$ Given: $$FV = 10000, R = 7, T = 4$$ Calculate: $$PV = \frac{10000}{1 + \frac{7 \times 4}{100}} = \frac{10000}{1 + 0.28} = \frac{10000}{1.28} = 7812.50$$ 5. What sum amounts to 6,720 in 2 years at 8% p.a. CI? Amount formula: $$A = P \left(1 + \frac{R}{100}\right)^T$$ Given $$A=6720, R=8, T=2$$ Find $$P$$: $$P = \frac{A}{(1 + \frac{R}{100})^T} = \frac{6720}{(1.08)^2} = \frac{6720}{1.1664} = 5760$$ 6. What annual payment will discharge a debt of 12,000 due in 3 years at 10% p.a.? This is an installment or annuity problem. Using formula for Present Value of an annuity: $$PV = P \times \frac{1 - (1 + r)^{-n}}{r}$$ Where: $$PV = 12000, r = 0.10, n = 3$$ Solve for $$P$$ (annual payment): $$12000 = P \times \frac{1 - (1 + 0.10)^{-3}}{0.10} = P \times 2.48685$$ $$P = \frac{12000}{2.48685} = 4825.41$$ 7. Calculate the amount due if 1,200 grows at CI 12% p.a. for 3 years. $$A = P \times (1 + \frac{R}{100})^T = 1200 \times (1.12)^3 = 1200 \times 1.404928 = 1685.91$$ 8. How much should be invested to get 20,000 after 5 years at 6% CI? Find Principal $$P$$ using: $$A = P \times (1 + \frac{R}{100})^T$$ Given $$A=20000, R=6, T=5$$ Calculate: $$P = \frac{20000}{(1.06)^5} = \frac{20000}{1.3382255776} = 14937.42$$