also, what formula would i have to use for this:
Effective Rate An advertisement for E*TRADE bank boasted "We're ahead of banks that had a 160-yr start," with an APY (or effective rate) of 2.01%.* The actual rate was not stated. Given that interest was compounded monthly, find the actual rate.
(1+x/12)^12 = 1.0201. Solve for x.
I personally would use and EXCEL spreadsheet and iterate till I found x.
To find the actual rate, you can use the formula provided:
(1 + x/12)^12 = 1.0201
Here's how to use the formula to solve for x:
1. Start by rearranging the equation to isolate x:
(1 + x/12)^12 = 1.0201
Taking the twelfth root of both sides gives:
1 + x/12 = (1.0201)^(1/12)
2. Subtract 1 from both sides:
x/12 = (1.0201)^(1/12) - 1
3. Multiply both sides by 12 to solve for x:
x = 12 * ((1.0201)^(1/12) - 1)
Calculating this expression will give you the actual rate (x) that corresponds to an annual percentage yield (APY) of 2.01% compounded monthly.
Alternatively, as you mentioned using an Excel spreadsheet, you could create a table with different values of x and corresponding values of (1 + x/12)^12. Using Excel's iterative calculation feature, you can find the value of x that yields a result closest to 1.0201.