# i want to calculate the annual effective interest rate given 10% per annum convertible quartely? question 9 Nov 2016 exam

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Question 9 please. I just want to know whats the effective interest rate of the given 10%.

answered Nov 9, 2018 by (140 points)
edited Nov 9, 2018 by hlulani

If you want the effective yearly of the 10% convertible quartely just use the standard conversion formula however if you're looking for the effective yearly interest rate of the investment this is bow you go about it

We first have to work how long it takes for the accumulated value FV>100000

$$70000(1+T\times1.25\% )=100000\implies T=34.2857$$

Therefore T=35 is the smallest value such that FV>100000

$$FV=70000\left(1+35\times 1.25\%\right)\left(1+\frac{10\%}{4}\right)^{\frac{120-35}{3}}=202557.6949$$

$$70000(1+i)^{10}=202557.6949\implies i=11.21031493\%$$

commented Nov 11, 2018 by (330 points)

Thank you. i was confused because the memo said otherwise but thats what i got

Since it's convertible quarterly, we know that it's a nominal amount - let's call it $$i^{(4)}$$. Thus, to make it effective quarterly we have to take $$\frac{i^{(4)}}{4}$$.
So now we have an effective quarterly rate and to convert it to effective annual we use $$\left(1+\frac{i^{(4)}}{4}\right)^4 =1+i$$