19% (a) compounded quarterly The given compound rate is equivalent to % simple interest.
Added by Manuel S.
Step 1
Let's think step by step. Show more…
Show all steps
Close
Your feedback will help us improve your experience
Adi S and 98 other Algebra educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Problem 2: An interest rate of 8% compounded semi-annually is how many percent if compounded quarterly. Given: Interest rate = 8% Compounding frequency = semi-annually Required: Interest rate compounded quarterly Solution: To find the interest rate compounded quarterly, we need to use the formula: (A = P(1 + frac{r}{n})^{nt}) Where: A = Final amount P = Principal amount r = Annual interest rate (as a decimal) n = Number of times interest is compounded per year t = Number of years In this case, we have: P = 1 (assuming a principal amount of 1 for simplicity) r = 8% = 0.08 (as a decimal) n = 2 (since interest is compounded semi-annually) t = 1 (since we are considering 1 year) Substituting these values into the formula, we get: (A = 1(1 + frac{0.08}{2})^{2 cdot 1}) Simplifying further: (A = (1 + 0.04)^2) (A = (1.04)^2) (A = 1.0816) Therefore, the interest rate compounded semi-annually is approximately 8.16% when compounded quarterly.
Adi S.
Find the effective rate when the stated rate is 19% and the interest is compounded quarterly. Write your answer using percent notation, including units.
Manisha S.
Breanna O.
Recommended Textbooks
Elementary and Intermediate Algebra
Algebra and Trigonometry
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD