Asked by Alyssa Cansler on May 02, 2024
Verified
Suppose you deposit $5,000 in a bank that pays 10 percent interest compounded twice a year. The actual annual interest rate you receive is
A) 10 percent.
B) 10.25 percent.
C) 11 percent.
D) 12 percent.
Compound Interest
Interest calculated on the initial principal of a deposit or loan, as well as on the accumulated interest of previous periods, leading to exponential growth of the amount over time.
- Distinguish between actual and nominal interest rates alongside understanding the principle of compound interest.
Verified Answer
MM
Marilyn MejiaMay 06, 2024
Final Answer :
B
Explanation :
The actual annual interest rate, also known as the effective annual rate (EAR), can be calculated using the formula for compound interest: EAR=(1+rn)n−1EAR = (1 + \frac{r}{n})^n - 1EAR=(1+nr)n−1 , where rrr is the annual interest rate (0.10 in this case) and nnn is the number of compounding periods per year (2 in this case). Plugging in the values, we get EAR=(1+0.102)2−1=(1.05)2−1=1.1025−1=0.1025EAR = (1 + \frac{0.10}{2})^2 - 1 = (1.05)^2 - 1 = 1.1025 - 1 = 0.1025EAR=(1+20.10)2−1=(1.05)2−1=1.1025−1=0.1025 or 10.25 percent.
Learning Objectives
- Distinguish between actual and nominal interest rates alongside understanding the principle of compound interest.