HighYield Savings advertises that an initial deposit of $2,000 at a 6% interest rate compounded semiannually will result in the balance reaching $5,000 in 10 years, with no need for additional deposits. Is this advertisement accurate?
Answer
A
True. The balance will reach 5 dollars comma 000 in 10 years at a 6 percent interest rate.
B
False. The balance will only double in 10 years at a 6 percent interest rate.
C
False. The balance will exceed 5 dollars comma 000 in 10 years at a 6 percent interest rate.
D
False. The balance will not reach 4 dollars comma 000 in 10 years at a 6 percent interest rate.
Explanation
With semiannual compounding, the interest rate per period is 6% ÷ 2 = 3%, and there are 10 × 2 = 20 periods. The balance is $2,000 × (1.03)^20, which is about $3,612. It falls short of $4,000, so the advertisement is inaccurate; choice D is correct.
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