Question

How many months would it take for a debt to grow by 40% if the annual interest rate is 2.4% with 6 compounding intervals per year? Hint: each compounding interval is 2 months long. Round your answer to the nearest month.

Answer 1

We have to find the no of months.

Since each compounding interval is 2 months long, so let no of such two months be n.

Now the effective interest rate (on compounding every two months) becomes 2.4/6 = 0.4 %.

Then after adding interest, the debt will become 140 % of itself. Hence we have

If debt is denoted by D, then we have

which gives

. Taking logarithm on base 10 we have

thus it will take 84.27 no. of two months i.e. 84.27*2 = 168.54 months which is around 169 months (answer)