Daniel is deciding between a compound interest account with a 3% annual rate, compounded quarterly, and a continuously compounded interest account at 2.75% annually for his $10,000 savings for 5 years. Which account will have a higher balance after 5 years? Compound Interest Formula: A=P(1+(r)/(n))^nt Continuously Compounded Interest Formula: A=Pe^rt The value of e , also known as Euler's number, is approximately 2.71828
Answer
A
Both accounts will have the same balance
B
More information is needed to decide
C
Continuously Compounded Interest Account
D
Compound Interest Account
Explanation
For quarterly compounding, the balance is $10,000(1 + 0.03/4)^(4×5), which is about $11,609. For continuous compounding, it is $10,000e^(0.0275×5), about $11,474. The quarterly compound interest account has the higher balance, so the correct choice is D, Compound Interest Account.
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