Interest: Compound Interest

Kate made a deposit in a savings account that pays 5% compound interest annually two years ago. If her current account balance is $1,323, how much did she deposit in the account?

Incorrect. [[snippet]] Add a 5% simple interest twice to this answer choice, and you will reach a number far exceeding the required balance of $1,323. This answer choice is too big.

Correct. [[snippet]] Calculate the simple interest as follows: - The first year will add 5% of $1,200, or $60 (quick calculation: 5% is half of 10% of $1,200). - For simple interest, the second year will add an additional 5%, or another $60, reaching a total interest of $120. Based on this, the balance after two years can be calculated as follows: >$$\text{Balance} = \$1{,}200+\$120 = \$1{,}320$$. Since 1,320 is very close to 1,323, and since the other answer choices are spread out, we can choose this as the correct answer with a high degree of certainty.

Incorrect. [[snippet]] Add a 5% simple interest twice to this answer choice, and you will reach a number far below the required balance of $1,323. This answer choice is too small.

Incorrect. [[snippet]] Add a 5% simple interest twice to this answer choice, and you will reach a number far below the required balance of $1,323. This answer choice is too small.

Incorrect. [[snippet]] Add a 5% simple interest twice to this answer choice, and you will reach a number far exceeding the required balance of $1,323. This answer choice is too big.

$1,000

$1,100

$1,200

$1,300

$1,400