[chuk1279]

Present Value Future Value Time Period Annual Interest Rate
$ 100 $ 118.76 3 years %
200 271.09 4 %
100 115.37 5 %

[fivestarstar]

Present Value Future Value Time Period Annual Interest Rate
$ 100 $ 118.76 3 years %
200 271.09 4 %
100 115.37 5 %

All answers are to three significant figures.

For simple interest, I = PRT / 100, i.e. R = 100I / PT

Therefore, the answer to the first question is 100 x (118.76-100) / (100 x 3) = 6.25, i.e. 6.25% p.a..

The answer to the second question is 100 x (271.09-200) / (200 x 4) = 8.89, i.e. 8.89% p.a.

The answer to the third question is 100 x (115.37-100) / (100x 5) = 3.07, i.e. 3.07% p.a.

For compound interest, A = P(1 + R/100)^n

First question:
118.76 = 100 (1 + R/100)^3
1.1876 = (1 + R/100)^3
cube root of 1.1876 = 1 + R/100
cube root of 1.1876 - 1 = R/100
100 (cube root of 1.1876 - 1) = R
5.90 = R
R = 5.90

Therefore, the interest rate is 5.90%.

Second question:
271.09 = 200 (1 + R/100)^4
1.35545 = (1 + R/100)^4
fourth root of 1.35545 = 1 + R/100
fourth root of 1.35545 - 1 = R/100
100 (fourth root of 1.35545 - 1) = R
7.90 or -208 (rejected) = R
R = 7.90

Therefore, the interest rate is 7.90%.


Third question:
115.37 = 100 (1 + R/100)^5
1.1537 = (1 + R/100)^5
fifth root of 1.1537 = 1 + R/100
fifth root of 1.1537 - 1 = R/100
100 (fifth root of 1.1537 - 1) = R
2.90 = R
R = 2.90


Therefore, the interest rate is 2.90%.