Simple and Compound Interest

Amount = P(1 + r/100)^n = 25000(1.06)^3 = 25000 * 1.191016 = 29775.40. Compound Interest = 29775.40 - 25000 = 4775.40.

Principal = 10000, Rate = 8% per annum, compounded semi-annually means 4% per half-year for 2 periods. Amount = 10000 * (1 + 0.04)^2 = 10000 * 1.0816 = 10816. Interest = 10816 - 10000 = 816.

Amount = Principal + Interest. Given Amount = 500 and Interest = 100, Principal = 500 - 100 = 400.

Since the annual incomes from both parts are equal, the ratio of the investments is inversely proportional to their interest rates, giving P1 : P2 = 6% : 4% = 3 : 2. This means Rs. 2,700 is invested at 4% and Rs. 1,800 at 6%, yielding an annual income of Rs. 108 from each part. The total annual income of Rs. 216 on a total investment of Rs. 4,500 results in an average interest rate of (216 / 4500) * 100 = 4.8%.

Amount = P(1 + r/100)^n. 968 = P(1 + 10/100)^2 = P(1.1)^2 = P(1.21). P = 968 / 1.21 = 800.

Difference for 2 years = P * (r/100)^2. 144 = P * (15/100)^2 = P * (3/20)^2 = P * 9/400. P = 144 * 400 / 9 = 16 * 400 = 6400.

Principal = 8000, Rate = 5% p.a. compounded half-yearly (2.5% per 6 months). Time = 1 year (2 periods). Amount = 8000 * (1.025)^2 = 8000 * 1.050625 = 8405. Interest = 8405 - 8000 = 405.

For 2 years, SI = 2 * P * R / 100 = 660, so P * R / 100 = 330. CI = P * (1 + R/100)^2 - P = 696.30. P * (2 * R/100 + (R/100)^2) = 696.30. Substituting 330: 2 * 330 + P * (R/100)^2 = 696.30. P * (R/100)^2 = 36.30. (P * R/100) * (R/100) = 36.30. 330 * (R/100) = 36.30. R = 11%.

For 2 years, SI = 2 * P * R / 100 = 400, so PR/100 = 200. CI = P(1 + R/100)^2 - P = 410. P(2R/100 + R^2/10000) = 410. 400 + P(R^2/10000) = 410. P(R/100)^2 = 10. 200 * (R/100) = 10. R/100 = 10/200 = 0.05. R = 5%.

Amount = P(1 + r/100)^n = 4800(1 + 0.06)^2 = 4800 * 1.1236 = 5393.28. Compound Interest = 5393.28 - 4800 = 593.28.

Present worth = Amount / (1 + r/100)^n. PW = 169 / (1 + 4/100)^2 = 169 / (1.04)^2 = 169 / 1.0816 = 156.25.

Principal = 16000, Time = 9 months (3 quarters), Rate = 20% p.a. = 5% per quarter. Amount = 16000 * (1.05)^3 = 16000 * 1.157625 = 18522. Interest = 18522 - 16000 = 2522.

A = P(1 + r/200)^(2n). 926.10 = 800(1 + 10/200)^(2n) = 800(1.05)^(2n). 926.1/800 = 1.157625. (1.05)^3 = 1.157625. So 2n = 3, n = 1.5 years.

The annual compound growth factor is 1 + 6.25/100 = 17/16. Therefore, the principal is 4913/(17/16)^3 = 4096 rupees.