Question - Calculating Compound Interest
Solution:
To solve the compound interest problem in the image, use the formula provided:A = P(1 + r/n)^(nt)Using the information given:- Herman puts $8,000.00 into the account.- The interest earned is 5% compounded annually.- We want to know the account balance after 9 years.In terms of the variables in the formula:- P = principal amount = $8,000.00- r = annual interest rate = 5% or 0.05 (as a decimal)- n = number of times the interest is compounded per year = 1 (since it is compounded annually)- t = the time the money is invested or borrowed for, in years = 9Now plug these values into the formula and solve:A = 8000(1 + 0.05/1)^(1*9)A = 8000(1 + 0.05)^9A = 8000(1.05)^9Now calculate the right side using a calculator:A = 8000 * 1.05^9 A ≈ 8000 * 1.551328216 (rounded to 9 decimal places)A ≈ 12,410.62572Rounding to the nearest cent, the final amount will be:A ≈ $12,410.63So, Herman will have approximately $12,410.63 in his account after 9 years.
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