Simple and Compound Interest

Principal = 12167, Interest = 3458, Amount = 15625. Time = 9 months = 3 quarters. A = P(1 + r/400)^3. 15625/12167 = (1 + r/400)^3. (25/23)^3 = (1 + r/400)^3. 25/23 = 1 + r/400 => 2/23 = r/400 => r = 800/23 = 34.78%. Matches 34.8%.

The increase in interest is due to the 3% higher rate over 2 years, which corresponds to an extra 6% of the principal X. Since this extra interest is Rs. 300, we have 0.06 * X = 300, which gives X = Rs. 5,000. Therefore, the value of 4X is 4 * 5,000 = Rs. 20,000.

Simple Interest = (P * R * T) / 100 = (800 * 5 * 6) / 100 = 240. Amount = Principal + Interest = 800 + 240 = 1040.

For compound interest, the amount after 2 years is A2 = P(1+r)^2 and after 1 year is A1 = P(1+r). Thus, (1+r) = A2/A1 = 2704/2600 = 1.04. P = A1 / 1.04 = 2600 / 1.04 = 2500.

Let P be the principal. (P * 0.15 * 1) - (P * 0.10 * 1) = 3500. 0.05P = 3500. P = 3500 / 0.05 = 70000.

Debt = Principal + Interest. 7500 + 7500*0.13*t = 8500 + 8500*0.11*t. 975t - 935t = 8500 - 7500. 40t = 1000. t = 25.

For 2 years, Simple Interest (SI) = 2*P*R = 7200, so PR = 3600. Compound Interest (CI) = P((1+R)^2 - 1) = P(2R + R^2) = 2PR + PR^2 = 8280. Substituting 2PR = 7200, we get 7200 + PR^2 = 8280, so PR^2 = 1080. Dividing PR^2 by PR gives R = 1080/3600 = 0.3 or 30%. Then P = 3600/0.3 = 12,000.

CI = P * ((1 + r/100)^n - 1) = 7500 * ((1.08)^2 - 1) = 7500 * (1.1664 - 1) = 7500 * 0.1664 = 1248.

Simple interest = 4000 for 2 years at 10% means principal = 20000. Compound interest for 2 years = 20000 * (1.1^2 - 1) = 20000 * 0.21 = 4200. The difference is 4200 - 4000 = 200.

Let x be the annual installment. The debt is discharged by the sum of the installments plus the interest on each. The first installment (paid at end of year 1) earns interest for 4 years, the second for 3, etc. Total = 5x + x * 0.09 * (4+3+2+1) = 5x + x * 0.09 * 10 = 5x + 0.9x = 5.9x. 5.9x = 4910. x = 4910 / 5.9 = 832.20.

Simple interest I = A - P = 1280 - 800 = 480. Using I = (P * R * T) / 100, we have 480 = (800 * R * 30) / 100, which simplifies to 480 = 240 * R, so R = 2%.

Interest for 3 years = 504 - 450 = 54. Interest per year = 18. Rate = (18/450) * 100 = 4%. For 615 in 2.5 years at 4%, interest = 615 * 0.04 * 2.5 = 61.5. Amount = 615 + 61.5 = 676.5.

Simple interest doubling in 2 years implies the rate is 50% per year. Using the compound interest formula A = P(1 + r/100)^t, where r = 50 and t = 2, the amount becomes P(1 + 0.5)^2 = 2.25P.

Interest for 5th year = Amount at end of 5 years - Amount at end of 4 years. Amount = 8000 * (1.1)^5 - 8000 * (1.1)^4 = 8000 * (1.1)^4 * (1.1 - 1) = 8000 * 1.4641 * 0.1 = 1171.28.

Year 1: 20000 at 20% compounded half-yearly (10% per 6 months). Amount = 20000 * (1.1)^2 = 24200. Interest = 4200. Year 2: 24200 at 20% compounded yearly. Amount = 24200 * 1.2 = 29040. Interest = 29040 - 24200 = 4840. Total interest = 4200 + 4840 = 9040.