Find the force of interest corresponding to effective rate of 8%?
Calculating Force of Interest
To calculate the force of interest corresponding to an effective rate of 8%, we can use the formula:
i = ln(1 + r/e)
Where:
- i = force of interest
- r = effective rate
- e = number of compounding periods per year
Substituting the Values
Substituting the values in the formula, we get:
i = ln(1 + 0.08/1)
i = ln(1.08)
i = 0.07696
Therefore, the force of interest corresponding to an effective rate of 8% is 0.07696 or approximately 7.7%.
Explanation
The force of interest is a measure of the rate at which an investment grows over time. It is the instantaneous rate of return or the rate of change of the investment's value with respect to time. The formula for calculating the force of interest depends on the effective rate and the number of compounding periods per year. The effective rate is the rate at which an investment grows over a year, taking into account the effect of compounding. The number of compounding periods per year refers to how many times the interest is compounded in a year.
In this case, we are given an effective rate of 8%, which means that an investment will grow by 8% over a year, taking into account the effect of compounding. Since there is only one compounding period per year, the number of compounding periods per year is 1. We can use the formula to calculate the force of interest, which tells us the rate at which the investment is growing at any given point in time.
The answer we get is approximately 7.7%, which means that the investment is growing at a rate of 7.7% per year, but this rate is not constant over time. The force of interest will change as the investment grows, and it will approach the effective rate as time goes on.