# Is there a way to convert from a monthly rate to annual?

This might seem like a silly question, but I'm trying to work out how much something will cost if I pay for it on my credit card instead of paying monthly to the company at their interest rate. The problem is that my online card account only shows the rates in monthly (1.2916%), and the company offering credit only show theirs annually (23.46%).

Do I simply multiply the monthly rate by 12 – giving me 15.49% - or does it not work like that?

If that's the case, then there's something very weird going on with my maths.

Their website states:

Deposit: 1 x £194.93
Monthly Payments: 11 x £78.63
Total: £1059.86
Instalments APR: 23.46%


If I try to work it out using their figures, I get a wildly different total!

(11 instalments * £78.63) = £864.93
£864.93 * 1.2346 = £1067.82

£1067.84 + £194.93 = £1262.77


Thanks, all.

• Do they have a daily rate of compounding somewhere on your account documents?
– user296
Jan 25 '11 at 0:23

Annual rate = monthly rate to the power of 12,

1.012916 ^ 12 = 1.1665, in other words 1.2916% monthly is 16.65% annual

this is just pure math, of course it depends how the interest accrues (daily, monthly) if there is any grace period, etc.

Unfortunately it's not as easy as just adding up the monthly interest rates - you have to take into account the effects of compounding (ie, interest on interest).

Unless my back-of-the-envelope calculation is completely wrong, you're looking at around 16.6% interest on the credit card.

The calculations others have provided are correct.

As for why the rates are expressed differently, who knows, but one observation is that with the monthly rate it's maybe a little less clear how much you're really paying in interest. 1.2% per month seems a little more benign than 16.65% per year, even though it's the same rate basically.

If $P$ is the principle and $m$ the monthly interest rate as a decimal, that is 6% then $m=.06$. Similarly for $y$ the yearly or annual interest rate. As one person had commented you have to account for how it is compounded. Monthly interest is compounded (or added back on to the principal on a monthly basis) where as yearly interest rate or APR is compounded annually. Really this does not matter because we can calculate a corresponding interest rate each.

P(m+1)^12n=P(y+1)^n where n is the number of years. This allows us to solve for m or y (P's cancel). Thus giving an exact formula relating the two. The results concure giving an annual interest rate of ~16.649 when the above formula is solved for y. Which would be a better rate then the store card or whatever.

• Why does mathjax not work? Aug 24 '15 at 1:45
• The cost to implement mathjax or latex didn't justify using it on Money.SE. It's not needed in 99% of questions or answers. You can always add an image to show what you wish. Aug 24 '15 at 4:48