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Suppose a mortgage has an interest rate of 6.5% per annum with monthly compounding. Find the per annum interest rate with quarterly compounding that would lead to the same effective annual rate.

I solved this one by:

$$r_eff = (1+\frac{0.065}{12}^{12})-1 =0.067%$$ $$(1+\frac{r}{4})^4-1=0.067$$ $$=(1+\frac{r}{4})= (1+0.067)^{\frac{1}{4}}$$

Solving for r, I get 6.52%

Now how would I find the rate with continuous compounding that would lead to the same effective annual rate? I understand that the formula is $$A=Pe^{rt}$$ How would I set up the problem?

1 Answers 1

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$A/P = e^{rt}$

You have already found the effective annual interest rate $=0.067$

Taking that to be correct, $e^r = 1+0.067$

Solve for $r$