Interest: Compound Interest

Anna took out a $10,000 loan to pay tuition fees. How much will she owe after one year if she does not make any payments and her bank charges 10% annual interest, compounded semiannually?

Incorrect. [[Snippet]]

Incorrect.

[[Snippet]]

Incorrect. [[Snippet]]

Incorrect. [[Snippet]]

If you're worried about answer choices C and B being relatively close, adjust your calculation into compound interest. Add 5% to the principal to find the balance after 6 months, and then add another 5% calculated out of the new balance: >$$\text{Balance after 6 months} = \$10{,}000 + \$500 = \$10{,}500$$. Add 5% of $10,500, which is $525: >$$\text{Balance after 1 year} = \$10{,}500 + \$525 = \$11{,}025$$.

Correct. [[Snippet]] Calculate simple interest and add it to the principal amount, and then eliminate any answer choice which is too far from the calculated value. >$$\text{Simple interest} = \text{Principal} \times \text{Interest rate} \times \text{Time}$$ >>>>$$= \$10{,}000 \times 0.1 \times 1$$ >>>>$$= \$1{,}000$$ Now add simple interest to the principal amount to find the balance after one year. >$$\text{Balance}= \$10{,}000 + \$1{,}000= \$11{,}000$$ Had the interest been simple, the balance would have been $11,000 after one year. Since the compound interest is only slightly greater than simple interest, this is sufficient to eliminate answer choices A, D, and E. At this point, answer choice B would be a good bet (since it's the closest answer choice to the simple interest value).

$11,000

$11,025

$11,075

$11,200

$11,250

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