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Polly has 1010 $\$ in an account that earns 5%5\% interest compounded annually. To the nearest cent, how much will she have 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. $\$____

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Q. Polly has 1010 $\$ in an account that earns 5%5\% interest compounded annually. To the nearest cent, how much will she have 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. Plug Values into Formula: Now, plug the values into the compound interest formula B=p(1+r)tB = p(1 + r)^t.p=$10p = \$10, r=0.05r = 0.05, and t=2t = 2 years.B=10(1+0.05)2B = 10(1 + 0.05)^2
  2. Calculate Inside Parentheses: Calculate the value inside the parentheses first. 1+0.05=1.051 + 0.05 = 1.05
  3. Raise to Power: Now raise 1.051.05 to the power of 22. (1.05)2=1.1025(1.05)^2 = 1.1025
  4. Multiply Principal Amount: Multiply the principal amount by the result.\newlineB=10×1.1025B = 10 \times 1.1025\newlineB=$(11.025)B = \$(11.025)
  5. Round Final Balance: Round the final balance to the nearest cent.$11.025\$11.025 rounds to $11.03\$11.03.

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