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Two investment are available.
Investment P offer interest of 5% per year compounded half-yearly for a period of 4 years.
Investment Q offer one interest payment 18% at the end of its 4 year life.What is the annual effective interest rate offered by each of the two investments ?
Investment P :
Investment Q :
P: The interest is 5/2 = 2.5% every six months.
So the effective annual rate is 1.025^2 – 1 = 0.050625 (or 5.0625% per year)Q: If the annual rate is R, then (1+R)^4 = 1.18
So R = (fourth root of 1.18) – 1 = 0.0422 (or 4.22% per year)If you invest $100 at interest of R per year, then by the end of 4 years the investment will have grown to $100 x (1+R)^4.
Alternatively if you invest $100 with one interest receipt of 18% at the end of 4 years, then it will have grown to $100 x 1.18.
So…..(1+R)^4 = 1.18
The rest of the solution follows as in my previous reply.
Hope that helps!
(You might find my free lecture on interest useful)
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