Monthly Rate vs Continuously Compounded Rate

A bank offers two alternative interest schedules for a savings account of \$100,000 locked in for 3 years. Which alternative should you choose?

(a) a monthly rate of 1%
(b) an annually, continuously compounded rate of 12%.

I want to calculate how much money we will have at the end of the third year, so I calculate:

(a) 100,000 * (1+1%)^36 = 143,076.878

(b) 100,000 * exp(3*12%) = 143,332.941

Are my claculations right? I am not sure if I get (a) correctly because I see that some people calculate it as 100,000 * (1+1%*36)

• This looks more like a homework problem than an actual problem of personal finance faced by the OP. If the OP can get an annual rate of 12% on a savings account these days, the OP should borrow as much as possible and put it into the bank account. I vote to close. Commented Dec 17, 2023 at 16:09
• @DilipSarwate: That very much depends on the country. In some unstable markets, 12% would be an atrociously low rate of return. Commented Dec 18, 2023 at 18:48