Question
Find the nominal rate of interest compounded monthly which is equivalent to an effective rate of 8.3% per annum.
Answers
GPT 3.5
To find the nominal rate of interest compounded monthly that is equivalent to an effective rate of 8.3% per annum, we can use the formula:
(1 + (r/n)) ^ n - 1 = 0.083
where r is the nominal interest rate, n is the number of compounding periods per year (12 for monthly compounding), and 0.083 is the equivalent effective annual interest rate.
Plugging in the values, we get:
(1 + (r/12)) ^ 12 - 1 = 0.083
Solving for r:
(1 + (r/12)) ^ 12 = 1.083
r/12 = 1.083 ^ (1/12) - 1
r/12 = 0.0074102
r = 0.0889224
Therefore, the nominal rate of interest compounded monthly equivalent to an effective rate of 8.3% per annum is approximately 8.89%.
(1 + (r/n)) ^ n - 1 = 0.083
where r is the nominal interest rate, n is the number of compounding periods per year (12 for monthly compounding), and 0.083 is the equivalent effective annual interest rate.
Plugging in the values, we get:
(1 + (r/12)) ^ 12 - 1 = 0.083
Solving for r:
(1 + (r/12)) ^ 12 = 1.083
r/12 = 1.083 ^ (1/12) - 1
r/12 = 0.0074102
r = 0.0889224
Therefore, the nominal rate of interest compounded monthly equivalent to an effective rate of 8.3% per annum is approximately 8.89%.