Simple and Compound Interest

The compound interest for the third year is simply the simple interest on the accumulated amount at the end of the second year. The amount after two years is 15000 * (1 + 0.10)^2 = 18150. Taking 10% of this amount gives the interest for the third year, which is 1815.

Investment = 21000 / 3 = 7000. Rate = 4% per annum, compounded quarterly = 1% per quarter. Time = 1 year = 4 quarters. Amount = 7000 * (1 + 0.01)^4 = 7000 * (1.01)^4 = 7000 * 1.04060401 = 7284.228. Savings = 7284.

Simple Interest = (P * R * T) / 100 = (10000 * 10 * 2) / 100 = 2000.

Compound interest formula: A = P(1 + r/100)^n. Given A/P = 1.404 and r=12. (1.12)^n = 1.404. Testing values: 1.12^2 = 1.2544, 1.12^3 = 1.4049. Thus, n is approximately 3 years.

CI = P * (1 + r/100)^n - P. CI = 1000 * (1 + 0.08)^4 - 1000 = 1000 * (1.08)^4 - 1000 = 1000 * 1.36048896 - 1000 = 360.49.

Compound interest is calculated as A = P(1 + r/100)^n. For P=100,000, r=13, and n=4, A = 100,000 * (1.13)^4 = 100,000 * 1.63047361 = 163,047.36. The interest is A - P = 63,047.36, which rounds to 63,000.

Difference for 3 years = P * (r/100)^2 * (3 + r/100). Difference = 2000 * (0.1)^2 * (3 + 0.1) = 2000 * 0.01 * 3.1 = 20 * 3.1 = 62.

Simple interest = Amount - Principal. If amount is twice the sum, interest = P. Formula: P = (P * R * 10) / 100. Solving for R: 1 = R * 10 / 100, so R = 10%.

Compound interest = P * ((1 + r/100)^n - 1) = 500 * ((1 + 0.02)^2 - 1) = 500 * (1.0404 - 1) = 500 * 0.0404 = 20.20.

Using A = P(1 + r/100)^n, we have 17640 = 16000(1 + r/100)^2. Dividing by 16000 gives 1.1025 = (1 + r/100)^2. Taking the square root gives 1.05 = 1 + r/100, so r = 5%.