Suppose that a money market fund pays a nominal rate of interest of 8.7 percent convertible monthly. What is the equivalent nominal rate convertible quarterly?
let the equivalent nominal rate compounded quarterly be j
Consider one year.
(1+.087/12)^12 = (1 + j/4)^4
1.00725^3 = 1+j/4
.051908068 = j/4
j = .087632274 or 8.763 %
To find the equivalent nominal rate convertible quarterly, we need to understand the concept of compounding frequency.
When interest is compounded monthly, it means that the interest is calculated and added to the principal amount every month. In this case, the nominal rate of interest is 8.7 percent convertible monthly.
To convert from a monthly compounding frequency to a quarterly compounding frequency, we need to know how many compounding periods are in each quarter. Since there are 3 months in a quarter, the interest will be compounded 3 times.
To find the equivalent nominal rate convertible quarterly, we can use the formula:
Nominal Rate Convertible Quarterly = (1 + Nominal Rate Convertible Monthly) ^ Number of Compounding Periods - 1
Let's calculate it step by step:
Step 1: Convert the nominal rate convertible monthly to a decimal form:
Nominal Rate Convertible Monthly = 8.7% = 0.087
Step 2: Calculate the equivalent nominal rate convertible quarterly:
Nominal Rate Convertible Quarterly = (1 + 0.087) ^ 3 - 1
Step 3: Simplify the calculation:
Nominal Rate Convertible Quarterly = (1.087) ^ 3 - 1
Step 4: Calculate the result:
Nominal Rate Convertible Quarterly = 1.087^3 - 1
Nominal Rate Convertible Quarterly = 1.26907 - 1
Nominal Rate Convertible Quarterly = 0.26907
Therefore, the equivalent nominal rate convertible quarterly is 26.907 percent.