Kim has money in a savings account that earns an annual interest rate of 4.1%, compounded monthly. What is the effective rate of interest on Kim's account? Round to the nearest hundredth of a percent.
monthly rate = .041/12 = .00341666..
let the effective annual rate be i
1 + i = (1 + .00341666..)^12
1+i = 1.0417783
i = .0417783 or
appr 4.18%
Thanks for the help and explanation!
To find the effective rate of interest, we need to consider the effects of compounding. The formula for the effective rate of interest is:
(1 + (r/n))^n - 1
where:
- r is the annual interest rate (expressed as a decimal)
- n is the number of compounding periods in one year
In this case, the annual interest rate is 4.1% (or 0.041 as a decimal) and the interest is compounded monthly, so the number of compounding periods in a year is 12.
Plugging the values into the formula:
(1 + (0.041/12))^12 - 1
Simplifying further:
(1 + 0.00341667)^12 - 1
Calculating:
(1.00341667)^12 - 1
(1.04239) - 1
0.04239
Finally, converting it back to a percentage:
0.04239 * 100 = 4.239%
Therefore, the effective rate of interest on Kim's account is approximately 4.24%.