9514 1404 393
Answer:
$6490.57
Step-by-step explanation:
The future value is given by the compound interest formula ...
A = P(1 +r/n)^(nt)
Principal P earns annual rate r compounded n times per year for t years.
Filling in the given values, we have ...
10000 = P(1 +0.065/2)^(2·7) = P(1.0325^14)
P = 10000/1.0325^14 ≈ 6390.5635
You would need to deposit $6390.57 into the account to have $10,000 in 7 years.
_____
Additional comment
Using the rounded-down result of the computation will result in a value after 7 years of $9,999.99, not quite $10,000. Rounding the computed value up to $6390.57 ensures the account balance will actually be $10,000.00 after 7 years.
If the balance is rounded to the nearest penny each time interest is added, then the balance after 7 years will be exactly $10,000.00. If there is no intermediate rounding, the resulting balance will be $10,000.01.
Most of the time, the answer key doesn't pay attention to details like this. Your expected answer may be $6390.56, or $6391 if rounded to dollars.
