Simple and Compound Interest

For 2 years, the amount is 24000 * (1.15)^2 = 31740. For the remaining 1/3 year, simple interest is applied: 31740 * (1 + 0.15 * 1/3) = 31740 * 1.05 = 33327. The interest is 33327 - 24000 = 9327.

1250 * (1 + r/100)^2 = 1250 + 102 = 1352. (1 + r/100)^2 = 1352 / 1250 = 1.0816. 1 + r/100 = sqrt(1.0816) = 1.04. r = 4%.

CI = P * (1 + r/100)^n - P = 1200 * (1.1)^2 - 1200 = 1200 * 1.21 - 1200 = 1452 - 1200 = 252.

If the amount doubles in 20 years, the growth factor after t years is 2^(t/20). For tripling, 2^(t/20) = 3, so t = 20 log2(3) ≈ 31.7 years. Rounded to the nearest whole year, this is 32 years.

For compound interest, the ratio of amounts for consecutive years (A2/A1) gives (1 + r/100). Here, 540/500 = 1.08. Thus, 1 + r/100 = 1.08, so r = 8%.

Using the compound interest formula A = P(1 + r/100)^n, 2P = P(1 + r/100)^15. 2 = (1 + r/100)^15. Solving for r gives approximately 4.73 percent.

Time = 5 years 4 months = 5 + 4/12 = 16/3 years. Amount = P + SI = P(1 + RT/100). 248 = Q(1 + 4.5 * (16/3) / 100) = Q(1 + 1.5 * 16 / 100) = Q(1 + 24/100) = Q(1.24). Q = 248 / 1.24 = 200.

Compound interest formula: A = P(1 + r/100)^n. A = 8000 * (1 + 5/100)^3 = 8000 * (1.05)^3 = 8000 * 1.157625 = 9261.

The simple interest for 3 years gives 3Pr = 90, so Pr = 30. The two-year compound interest is 2Pr + Pr^2 = 63, giving Pr^2 = 3 and r = 0.1. Therefore, P = 30/0.1 = Rs 300.

For quarterly compounding, the rate is 20%/4 = 5% per quarter, and 9 months equals 3 quarters. The amount is 8000 * (1.05)^3 = 8000 * 1.157625 = 9261. The compound interest is 9261 - 8000 = 1261.

CI for 2 years = 10000 * (1.04)^2 - 10000 = 816. For the remaining 1/2 year, interest = (10000 + 816) * 0.04 * 0.5 = 10816 * 0.02 = 216.32. Total CI = 816 + 216.32 = 1032.32, which rounds to 1032.

For 2 years, SI = 2 * (P * R / 100) = 400, so P * R / 100 = 200. CI = P * (1 + R/100)^2 - P = 410. Substituting P*R/100 = 200 into the CI formula: 200 + P * (R/100)^2 = 410, so P * (R/100)^2 = 210. Dividing the two equations: (P * R^2 / 10000) / (P * R / 100) = 210 / 200, so R/100 = 1.05, R = 5%.

Simple Interest = 1000 * 0.10 * 4 = 400. Compound Interest = 1000 * (1.1^4 - 1) = 1000 * (1.4641 - 1) = 464.10. The difference is 464.10 - 400 = 64.10.

Statement I: SI = 2000 for 5 years at 5000 principal means SI = 400 per year. Rate = (400/5000)*100 = 8%. With rate and principal, CI for 2 years can be calculated. Statement II: CI and SI are same for 1 year, which is always true for any rate, so it provides no info. Statement III: Amount > double in 10 years gives a range for the rate, but not a specific value. Thus, only I is sufficient.