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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.I explain in my previous reply how we get the EAR for Wye and I assume that what you have typed (1.200.25) is copied from a book.
1.200 is 1 + 0.2 (0.2 is the same as 20%). We do not multiply 1.20 by 0.25 (f that is what is in your book then it is a typing error). What they mean is 1.20 ^ 0.25 because taking something to the power of 0.25 is another way of writing to take the fourth root and we take the fourth root for the reason explained in my previous reply.
Have you watched my free lectures on interest? The lectures are a complete free course for Paper MA and cover everything needed to be able to pass the exam well.
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