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=1400(1.05)^(2t)
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, P is the principal or initial amount, r is the annual interest rate written in decimal form, t is the time in years, and n is the number of times the interest is compounded in one year. Let's pay close attention to the given exercise.
We can immediately identify P as 1400. Also, the annual interest rate, written as a decimal number, is 0.1. Finally, since the interest is compounded semiannually and there are 2 halves of a year in one year, we have that n= 2. Let's substitute these values into the formula and simplify.
