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We begin by finding the nominal convertible quarterly interest rate i or effective quarterly rate i/4 either way.

We find the effective quarterly rate as (i/4) for the first 4 years (16 quarters). The effective monthly rate is (3i/12) = i/4 as well for the next 10 years (120 months).

Thus:

\(80 000 = 20 000*(1+i/4)^{16} * (1+3i/12)^{120} \)

\(80 000 = 20 000*(1+i/4)^{16} * (1+i/4)^{120} \)

\(80 000 = 20 000*(1+i/4)^{136} \)

\(i/4 = 0.01024547\) effective quarterly

\(i = 0.04098188\) nominal convertible quarterly

Thus, after 3 years (12 quarters) we accumulate:

\(FV = 20 000*(1+i/4)^{12} = R22 602.32\)

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Hi Mnem

This question is a nice example of a problem which appears to be very complicated, but once you start working on it, a very elegant solution appears. That being said, I think it will be beneficial for you to find this solution on your own, however, let me give you a hint to help you on your way.

Remember that if we have an interest rate \(i\) which is convertible \(n^{th}\)ly then the accumulation factor for an amount \(A\) over \(z\) years is given by:

$$ FV = A(1 + \frac{i}{n})^{n\times z}$$

Try using the above accumulations and see what appears. If you would like further help, simply comment on this answer.

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The picture is very unclear, please use Snipping Tool so you can highlight the specific question and post just that. Might make it easier to read.

Thanks!