Answer:
To determine the equivalent nominal rate of interest with monthly compounding for a given interest rate of 10% compounded quarterly, we can use the concept of effective interest rates. The effective interest rate takes into account the compounding frequency and provides a measure of the true interest earned or paid over a specific period.
To calculate the equivalent nominal rate with monthly compounding, we need to convert the quarterly interest rate to a monthly rate. Since there are four quarters in a year, each quarter will have an interest rate of 10%/4 = 2.5%.
To find the equivalent monthly interest rate, we can use the formula:
(1 + r)^n = (1 + i)^m
Where:
- r is the monthly interest rate
- n is the number of months in a year (12)
- i is the quarterly interest rate (2.5%)
- m is the number of quarters in a year (4)
Substituting the values into the formula:
(1 + r)^12 = (1 + 0.025)^4
Simplifying:
(1 + r)^12 = (1.025)^4
Taking the twelfth root on both sides:
1 + r = (1.025)^(4/12)
Calculating:
1 + r = 1.020161051
Subtracting 1 from both sides:
r = 0.020161051
Converting to a percentage:
r ≈ 2.0161051%
Therefore, the equivalent nominal rate of interest with monthly compounding is approximately 2.0161051%.
Step-by-step explanation: