1. Calculate Simple Interest (SI) on 5,000 for 3 years at 6% p.a. SI formula is $SI = \frac{P \times R \times T}{100}$ Here, $P=5000$, $R=6$, $T=3$ $$SI = \frac{5000 \times 6 \times 3}{100} = 900$$ 2. Find Compound Interest (CI) on 8,000 for 2 years at 5% compounded annually. CI formula is $A = P \left(1 + \frac{R}{100}\right)^T$ Then, $CI = A - P$ Here, $P=8000$, $R=5$, $T=2$ $$A = 8000 \left(1 + \frac{5}{100}\right)^2 = 8000 \times 1.1025 = 8820$$ $$CI = 8820 - 8000 = 820$$ 3. A bill of 60,000 is discounted at 6% p.a. for 3 months before maturity. Find discount. Discount $D = \frac{P \times R \times T}{100}$ with $T$ in years $T = \frac{3}{12} = 0.25$ years, $P=60000$, $R=6$ $$D = \frac{60000 \times 6 \times 0.25}{100} = 900$$ 4. Find present value of 10,000 due in 4 years at 7% p.a. SI. Present value $PV = \frac{A}{1 + \frac{R \times T}{100}}$ Here, $A=10000$, $R=7$, $T=4$ $$PV = \frac{10000}{1 + \frac{7 \times 4}{100}} = \frac{10000}{1 + 0.28} = \frac{10000}{1.28} = 7812.50$$ 5. What sum amounts to 6,720 in 2 years at 8% p.a. CI? $A = P \left(1 + \frac{R}{100}\right)^T$, solve for $P$ $A=6720$, $R=8$, $T=2$ $$6720 = P (1.08)^2 = P \times 1.1664$$ $$P = \frac{6720}{1.1664} = 5760$$ 6. What annual payment will discharge a debt of 12,000 due in 3 years at 10% p.a.? This is an annuity problem. Annuity payment $P = \frac{D \times r}{1 - (1 + r)^{-n}}$ Where $D=12000$, $r=0.10$, $n=3$ $$P = \frac{12000 \times 0.10}{1 - (1.10)^{-3}} = \frac{1200}{1 - 0.7513} = \frac{1200}{0.2487} = 4823.53$$ 7. Calculate the amount due if 1,200 grows at CI 12% p.a. for 3 years. $A = P \left(1 + \frac{R}{100}\right)^T$ $P=1200$, $R=12$, $T=3$ $$A = 1200 \times 1.12^3 = 1200 \times 1.404928 = 1685.91$$ 8. How much should be invested to get 20,000 after 5 years at 6% CI? $A = P \left(1 + \frac{R}{100}\right)^T$ solve for $P$ $A=20000$, $R=6$, $T=5$ $$20000 = P \times 1.3382256$$ $$P = \frac{20000}{1.3382256} = 14943.57$$