The formula that gives the balance y of an account earning compound interest is y=P( 1+ rn )^(nt), where P is the principal, r is the annual interest rate, t is the time in years, and n is the number of times the interest is compounded in one year.
y=2000(1.0125)^(4t)
Practice makes perfect
Compound interest is the interest earned on the principal and on previously earned interest. Let's recall the formula that gives the balance y of an account earning compound interest.
y= P( 1+r/n )^(n t)
In this formula ${\color{#0000FF}{P}}is the ''principal'' or initial amount,{\color{#FD9000}{r}}is the annual interest rate written in decimal form,{\color{#A800DD}{t}}is the time in years, and{\color{#009600}{n}}is the number of times the interest is compounded in one year. Let's pay close attention to the given exercise.
'"`UNIQ--statementbox-00000001-QINU`"'
We can immediately identify{\color{#0000FF}{P}}as{\color{#0000FF}{2000}}.Also, the annual interest rate, written as a [[Concept:Decimal Numbers|decimal number]], is{\color{#FD9000}{0.05}}.Finally, since the interest is compounded quarterly, we have that{\color{#009600}{n}}={\color{#009600}{4}}.$ Let's substitute these values into the formula and simplify.
