Simple and Compound Interest

For compound interest, A = P(1 + r/100)^n. Here A = 4P, n = 2. 4P = P(1 + r/100)^2. 4 = (1 + r/100)^2. Taking the square root, 2 = 1 + r/100. r/100 = 1, so r = 100%.

A = P(1 + r/100)^n. 1352 = P(1 + 4/100)^2 = P(1.04)^2 = P(1.0816). P = 1352 / 1.0816 = 1250.

Compound interest = P * ((1 + r/100)^n - 1) = 800 * ((1 + 5/100)^3 - 1) = 800 * (1.05^3 - 1) = 800 * (1.157625 - 1) = 800 * 0.157625 = 126.10.

Amount = P(1 + r/100)^n. For 2.5 years, A = 800 * (1 + 0.05)^2 * (1 + 0.05 * 0.5) = 800 * 1.1025 * 1.025 = 904.05.

Simple interest for 2 years = 40, so SI for 1 year = 20. Compound interest for 2 years = 40.80. The extra 0.80 is the interest on the first year's interest. Rate = (0.80 / 20) * 100 = 4%.

Amount after 2 years = P(1+r)^2 = 2809. Amount after 3 years = P(1+r)^3 = 2977.54. Dividing the two: (1+r) = 2977.54 / 2809 = 1.06. So r = 0.06 or 6%.

Interest for year 1 = 100 * 0.05 = 5. Amount after year 1 = 105. Interest for year 2 = 105 * 0.06 = 6.30. Total interest = 5 + 6.30 = 11.30.

Amount = P * (1 + r/100)^n. 2809 = P * (1 + 0.06)^2 = P * (1.06)^2 = P * 1.1236. P = 2809 / 1.1236 = 2500.

Compound interest formula is A = P(1 + r/100)^n. For P=10000, r=7, n=5, A = 10000 * (1.07)^5 = 10000 * 1.4025517 = 14025.517. The interest is A - P = 4025.5.

The question asks for the compound interest amount but mentions the simple interest method, which is contradictory. Calculating compound interest for 75,000 at 2.5% for 2 years: 75,000 * (1 + 0.025)^2 = 75,000 * 1.050625 = 78,796.875.

Compound amount = 2500 * (1 + 12/100)^2 = 2500 * 1.12^2 = 2500 * 1.2544 = 3136. A paid 2936 + watch = 3136. Watch = 3136 - 2936 = 200.