Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Valeria deposited 8080 $\$ in an account earning 5%5\% interest compounded annually. To the nearest cent, how much interest will she earn in 22 years? Use the formula B=p(1+r)tB = p(1 + r)^t, where BB is the balance (final amount), pp is the principal (starting amount), rr is the interest rate expressed as a decimal, and tt is the time in years. $\$____

Full solution

Q. Valeria deposited 8080 $\$ in an account earning 5%5\% interest compounded annually. To the nearest cent, how much interest will she earn in 22 years? Use the formula B=p(1+r)tB = p(1 + r)^t, where BB is the balance (final amount), pp is the principal (starting amount), rr is the interest rate expressed as a decimal, and tt is the time in years. $\$____
  1. Convert to Decimal: Convert the interest rate from a percentage to a decimal by dividing by 100100. 5%=5100=0.055\% = \frac{5}{100} = 0.05
  2. Plug Values into Formula: Plug the values into the compound interest formula B=p(1+r)tB = p(1 + r)^t. Here, p=$80p = \$80, r=0.05r = 0.05, and t=2t = 2. B=80(1+0.05)2B = 80(1 + 0.05)^2
  3. Calculate Inside Parentheses: Calculate the value inside the parentheses first. 1+0.05=1.051 + 0.05 = 1.05
  4. Raise to Power: Raise 1.051.05 to the power of 22. (1.05)2=1.1025(1.05)^2 = 1.1025
  5. Multiply Principal Amount: Multiply the principal amount by the result from the previous step.\newlineB=80×1.1025B = 80 \times 1.1025
  6. Perform Multiplication: Perform the multiplication to find the balance after 22 years. B=80×1.1025=88.20B = 80 \times 1.1025 = 88.20

More problems from Compound interest