The effective rate of interest corresponding a nominal rate of 7% p.a. convertible quarterly is:
7.1859
To find the effective rate of interest corresponding to a nominal rate of 7% p.a. convertible quarterly, you need to use the formula for effective interest rate.
The formula for effective interest rate (i) can be calculated using the formula:
i = (1 + r/n)^n - 1
Where:
i = effective interest rate
r = nominal interest rate
n = number of conversion periods per year (in this case, 4 because it is convertible quarterly)
Substituting the given values into the formula:
i = (1 + 0.07/4)^4 - 1
Now, let's calculate this using a calculator or computer:
(1 + 0.07/4)^4 = 1.0175
i = 1.0175 - 1
i = 0.0175
So, the effective rate of interest corresponding to a nominal rate of 7% p.a. convertible quarterly is 1.75% (0.0175 expressed as a percentage).
To find the effective rate of interest corresponding to a nominal rate of 7% p.a. convertible quarterly, follow these steps:
Step 1: Convert the annual nominal rate to a quarterly nominal rate. Since there are 4 quarters in a year, divide the annual nominal rate by 4.
7% / 4 = 1.75%
Step 2: Convert the quarterly nominal rate to a decimal by dividing it by 100.
1.75% / 100 = 0.0175
Step 3: Add 1 to the quarterly nominal rate expressed as a decimal.
1 + 0.0175 = 1.0175
Step 4: Raise the sum to the power of the number of compounding periods in a year. In this case, since the nominal rate is convertible quarterly, the compounding periods in a year would be 4.
(1.0175)^4 ≈ 1.071675034
Step 5: Subtract 1 from the result and multiply by 100 to convert it to a percentage to obtain the effective rate of interest.
(1.071675034 - 1) × 100 ≈ 7.1675034%
Therefore, the effective rate of interest corresponding to a nominal rate of 7% p.a. convertible quarterly is approximately 7.17%.