FutureSecure Bank claims that by depositing $5,000 in a savings account with a 7% annual interest rate compounded quarterly, the amount will grow to $10,000 in 7 years without any additional deposits. Is this claim true?
Answer
A
False. The amount will not reach 10 dollars comma 000 in 7 years at a 7 percent interest rate.
B
False. The amount will exceed 10 dollars comma 000 in 7 years at a 7 percent interest rate.
C
True. The amount will grow to exactly 10 dollars comma 000 in 7 years at a 7 percent interest rate.
D
False. The amount will not reach 8 dollars comma 000 in 7 years at a 7 percent interest rate.
Explanation
Use the compound-interest formula: 5,000 × (1 + 0.07/4)^(4 × 7), since interest is compounded quarterly for 7 years. This gives about $8,120, which is more than $8,000 but less than $10,000. So the claim is false; choice A correctly says the balance will not reach $10,000.
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