Simple and Compound Interest

CI = P * ((1 + r/100)^n - 1). CI = 2000 * ((1.05)^2 - 1) = 2000 * (1.1025 - 1) = 2000 * 0.1025 = 205.

Calculate interest for 2 years at 8% using A = P(1 + 0.08)^2 = 31250 * 1.1664 = 36450. The interest for 2 years is 5200. For the remaining 3/4 year, interest is calculated on 36450 at 8% simple interest for 0.75 years: 36450 * 0.08 * 0.75 = 2187. Total interest = 5200 + 2187 = 7387.

The amount after 3 years at 10% compound interest is 1000 * (1.1)^3 = 1000 * 1.331 = 1331. The compound interest is 1331 - 1000 = 331.

Using the compound interest formula, A = P(1 + r/100)^n, we have 2226.05 = 2000(1 + r/100)^2. Dividing both sides by 2000 gives (1 + r/100)^2 = 1.113025. Taking the square root of both sides yields 1 + r/100 = 1.055, which gives r = 5.5%.

For 2 years, SI = 2Pr = 200, so Pr = 100. CI = P(1+r)^2 - P = 2Pr + Pr^2 = 210. Substituting Pr=100: 200 + 100r = 210, so 100r = 10, r = 0.1 (10%). Then P * 0.1 = 100, so P = 1000.

Amount = P(1 + r/100)^n. 3528 = 3200(1 + 0.05)^n. 3528/3200 = (1.05)^n. 1.1025 = (1.05)^n. Since 1.05^2 = 1.1025, n = 2 years.

Principal = 100, Rate = 10% per annum, compounded half-yearly (5% per half-year). For 1 year (2 periods), Amount = 100 * (1 + 0.05)^2 = 100 * 1.1025 = 110.25. Compound Interest = 110.25 - 100 = 10.25.

Let the instalment be X. 11000 = X / (1.2) + X / (1.2)^2. 11000 = X * (1/1.2 + 1/1.44) = X * (1.2 + 1) / 1.44 = X * 2.2 / 1.44. X = 11000 * 1.44 / 2.2 = 5000 * 1.44 = 7200.

Rate = 50/3%. Annual payment P satisfies P/(1+r) + P/(1+r)^2 + P/(1+r)^3 = 7620. Solving this for P gives 3430.

Amount after 1 year = 5600 * 1.1 = 6160. Interest for the remaining half year = 6160 * 0.1 * 0.5 = 308. Total interest = 560 + 308 = 868.

Let annual payment be x. 16400 = x/(1.05) + x/(1.05)^2. 16400 = x(1/1.05 + 1/1.1025) = x(1.05/1.1025 + 1/1.1025) = x(2.05/1.1025). x = 16400 * 1.1025 / 2.05 = 8820.

For compound interest, A = P(1+r)^t. 2P = P(1+r)^20, so (1+r)^20 = 2. We want 3P = P(1+r)^t, so (1+r)^t = 3. Taking logs: t * log(1+r) = log(3) and 20 * log(1+r) = log(2). t = 20 * log(3)/log(2) = 20 * 0.4771/0.3010 = 31.69 years.

For a loan P repaid in two equal annual installments X at interest rate r, the formula is P = X / (1+r) + X / (1+r)^2. With P=10500 and r=0.1, 10500 = X/1.1 + X/1.21. Solving for X gives 6050.