Asked by Tasha Barnes on May 07, 2024
Verified
What effective rate of interest is equivalent to a nominal rate of 19.214% compounded monthly?
A) 1.210%
B) 21.000%
C) 14.530%
D) 22.000%
E) 17.704%
Effective Rate
The actual annual interest rate that accounts for compounding over a given period, providing a true reflection of the financial cost or benefit.
Nominal Rate
The stated interest rate of a financial instrument, without adjustment for inflation or compounding frequencies.
Compounded Monthly
The method of computing interest that includes both the original amount and the interest accrued over past months, applied each month.
- Evaluates the impact of changes in interest rates on finance charges and the actual rates of interest.
Verified Answer
NP
Nayda PeaceMay 11, 2024
Final Answer :
B
Explanation :
The effective rate of interest can be calculated using the formula for converting a nominal rate compounded monthly to an effective annual rate: E=(1+rn)n−1E = (1 + \frac{r}{n})^n - 1E=(1+nr)n−1 , where EEE is the effective annual rate, rrr is the nominal annual rate, and nnn is the number of compounding periods per year. Plugging in the given nominal rate of 19.214% (or 0.19214 as a decimal) compounded monthly (n = 12), we get E=(1+0.1921412)12−1E = (1 + \frac{0.19214}{12})^{12} - 1E=(1+120.19214)12−1 , which approximately equals 0.21 or 21% when converted to a percentage.
Learning Objectives
- Evaluates the impact of changes in interest rates on finance charges and the actual rates of interest.