Annual percentage interest rate

Question

An annual percentage interest rate of $30\%$ is equivalent to a monthly compound interest rate closest

A) $2.02\%$

B) $2.21\%$

C) $2.50\%$

D) $2.66\%$

The answer is B
Can anyone tell me how?

The idea here is to equate the principal at time $t$ if the account earns an annual percentage rate of $30%$ with the principal at time $t$ if the account earns an annual percentage rate of $100r%$ compounded monthly. — N. F. Taussig, May 18 '18 at 09:39

score 0 · Answer 1 · answered Apr 02 '18 at 11:17

0

Note that

$$(1+0.0221)^{12}\approx 1.30$$

answered Apr 02 '18 at 11:17

user

Can you show the solution please. – AYESHA Apr 02 '18 at 11:28
you can check it by calculator – user Apr 02 '18 at 11:29
It's there another way to solve it without the calculator – AYESHA Apr 02 '18 at 11:33
No you need to calculate in some way, also binomial approximation $(1+x^a)\approx 1+ax$ leads to the wrong result 2.50%. The calculation is simple, we just need to iterate 12 times the multiplication by (1.0221). – user Apr 02 '18 at 11:38

1 Answers1