Asked by Bennie Raymond on Jul 21, 2024
Verified
A so-called friend has offered to loan you $1,000 for one year. At the end of the year you must pay your friend $2,000. What is the APR on this loan if interest is compounded daily?
A) 50.00%
B) 69.38%
C) 81.33%
D) 96.30%
E) 100.00%
APR
Annual Percentage Rate, the annual rate charged for borrowing or earned through an investment.
Compounded Daily
A method where interest is calculated and added to the account balance every day, leading to higher yields over time.
Loan
Borrowed money that is typically repaid with interest.
- Assess the effective annual rate (EAR) for a range of compounding frequencies.
Verified Answer
IC
Ivonne CortesJul 27, 2024
Final Answer :
B
Explanation :
The APR can be calculated using the formula for compound interest: A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount ($1,000), r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the time the money is invested for in years. In this case, A = $2,000, P = $1,000, n = 365 (since interest is compounded daily), and t = 1 year. Rearranging the formula to solve for r gives us the APR. Plugging the numbers into the formula and solving for r gives an APR of approximately 69.38%.
Learning Objectives
- Assess the effective annual rate (EAR) for a range of compounding frequencies.
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