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Forums › Ask ACCA Tutor Forums › Ask the Tutor ACCA MA – FIA FMA › Compound interest rate
could you please explain it please thanks in advance
An investor has the choice between two investments. Investment Exe offers interest of 4% per year compounded semi-annually for a period of three years. Investment Wye offers one interest payment of 20% at the end of its four-year life.
What is the annual effective interest rate offered by the two investments?
Investment Exe Investment Wye
A 4·00%. 4·66%
B 4·00% 5·00%
C 4·04% 4·66%
D 4·04% 5·00%
The correct answer is C. The answer can be arrived at by calculation (Investment Exe annual effective return = 1.022 – 1 = 0.0404 or 4.04% and investment Wye annual effective return = 1.200.25 – 1 = 0.0466 or 4.66%). Alternatively the answer can be “reasoned” out: investment Exe’s semi annual compounding must result in a higher effective annual rate than 4% (2 × 2%) and a 20% return over a 4 year period must have an effective annual rate of less than 5% (20% ÷ 4 years) when the compounding effect is allowed for. Just over 32% of candidates incorrectly selected option D . This suggests that although most candidates can convert a sub annual interest rate into an effective annual rate, many find it difficult to convert a multi year rate into an effective annual rate.
Have you watched my free lectures on interest rates? (The lectures are a complete free course for Paper F2 and cover everything needed to be able to pass the exam well).
In the case of Exe the interest is 4/2 = 2% every six months. There are two six months in a year, and therefore the effective annual interest rate is 1.02^2 = 1 = 0.0404 or 4.04% per year.
In the case of Wye, if the interest rate is R per year, then the interest over 4 years will be (1+R)^4 – 1, and this must be equal to 0.20 (20%)
(1+R)^4 – 1 = 0.20
So, (1+R)^4 = 1.20
Therefore 1+R = fourth root of 1.20 = 1.0466
Therefore R = 0.0466 or 4.66% per year.