Calculating Compound Interest
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 = 9
Now plug these values into the formula and solve:
A = 8000(1 + 0.05/1)^(1*9)
A = 8000(1 + 0.05)^9
A = 8000(1.05)^9
Now calculate the right side using a calculator:
A = 8000 * 1.05^9
A ≈ 8000 * 1.551328216 (rounded to 9 decimal places)
A ≈ 12,410.62572
Rounding to the nearest cent, the final amount will be:
A ≈ $12,410.63
So, Herman will have approximately $12,410.63 in his account after 9 years.
