3 years ago

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Mathematics

1 answer:

Mnenie [13.5K]3 years ago

8 0

What is the math problem?

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$10,000 at an annual rate of 7%, compounded semi-annually, for 2 years

forsale [732]

Answer:

$\$13,107.96$

Step-by-step explanation:

Since interest is compounded semi-annually (half a year or 6 months), in a spawn of 2 years, the interest will have been compounded 4 times. As given in the problem, each time the interest is compounded, the new balance will be 107% or 1.07 times the amount of the old balance.

Therefore, we can set up the following equation to find the new balance after 2 years:

$\text{New balanace}=10,000\text{ (old balance)}\cdot 1.07\cdot 1.07\cdot 1.07\cdot 1.07,\\\text{New balanace}=10,000\cdot 1.07^4=\boxed{\$13,107.96}$