Question

A bank advertises that it pays interest on saving accounts at the rate of 9.25% compounded daily.

(a) Find the effective rate if the bank uses 360 days in determining the daily rate.

Answer 1

What is the effective rate if 365 days are used?

Answer 2

Casey, I hate to say it, but.... most of us here don't know much about economics. :/ I don't think you'll find much help here. That's not to say you shouldn't try, but I think it'll take some time for someone to show up. I myself dropped economics after my second test.

Answer 3

The formula for calculating compound interest is: \[A_t = A_0 (1 + d) ^ {t} \] where A(0) is the amount we initially invest, d is the daily interest rate, and A(t) is the amount we have after t periods of compounding.

In your example, the daily interest rate the bank pays is 9.25%/360 days = 0.02569%. T is the number of periods this gets compounded for, so if we want to calculate the effective yearly rate, we use 365. Putting it all together (assuming we invest $100 at the start of the year, for simplicity):\[A_t=$100\times(1+0.02569/100)^{365}=$109.83\] to the nearest cent. So the bank has paid us a total of $9.83 of interest, and the effective rate is 9.83%.

If the bank used 365 days, we simply divide 9.25% by 365 to get the daily rate instead, giving 9.69% instead, which is not a huge difference!