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How much would you need to deposit into an account that pays 6.5% interest compounded semiannually to have $10,000 after 7 years?

2 Answers

0 votes

Answer:

6390.56

Explanation:


AV=PV(1+(i)/(n))^(nt)\\10000=x(1+(.065)/(2))^(7*2)\\10000=1.564807232*x\\6390.53=x

User Mannopson
by
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1 vote

9514 1404 393

Answer:

$6490.57

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.

User Bedasso
by
8.3k points

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