Question

Suppose you deposit $2,000 in a savings account that pays interest at an annual rate of 4%. If no money is added or withdrawn, determine how much would be in the account after 3 years.
$1,847.12
$2,249.73
$7,432.62
$7,876.25

Answer 1

Hi there! Based off of the answer choices, I think this has to do with compound interest. The formula for compound interest is P(1 + r)^t. P = principal (initial amount), r = rate (percentage), and t = time (years). The rate is 4%. 4% is 0.04 in decimal form. Add 1 to that number in order to get 1.04. Now, raise that decimal to the 3rd power, because that is being compounded annually and it is being compound 3 times, because three years will have passed. 1.04³  is 1.124864. Don't delete that decimal or round. Now, multiply that number by the principal, which is 2,000. When you do that, you get 2,249.728 or 2,249.73 when rounded to the nearest hundredth. If no money is withdrawn, there will be $2,249.73 in 3 years. The answer is B.

Note: For the formula, you just follow the order of operations. In order words, convert the rate into decimal form, add 1 to it, then raise it to the power, based on the number of years. Don't delete the decimal from the calculator or round. Multiply that decimal by the principal to get your answer. You always solve compound interest questions like these with that formula. There is something extra that applies on some occasions, but we don't need it for this problem.