If the APR is 7% with monthly compounding, compute the quarterly rate
let the quarterly rate be i
then (1+i)^4 = (1+.07/12)^12
take 4th root of both sides
1+i = 1.0058333..^4
1+i = 1.023538
i = .023538 or 2.3538% per quarter
times 4, gives us
9.4153% per annum compounded quarterly.
Monthly rate=0.07/12=0.005833
Quarterly rate=(1+Monthly rate)^3-1
=(1+0.005833)^3-1
=1.017601-1
=0.017601
=1.76%
To compute the quarterly rate from an annual interest rate with monthly compounding, you need to divide the annual interest rate by 12 (the number of months in a year) and then multiply it by 3 (the number of months in a quarter).
Here's the step-by-step calculation:
1. Convert the APR to a decimal form by dividing it by 100. In this case, 7% becomes 0.07.
2. Divide the annual rate by 12 to get the monthly rate. 0.07 / 12 = 0.00583.
3. Multiply the monthly rate by 3 to get the quarterly rate. 0.00583 * 3 = 0.0175, or 1.75%.
Therefore, the quarterly rate with an APR of 7% and monthly compounding is 1.75%.