Find the balance on an account if you invest $100 at 5% for 10 years compounded annually.
100 (1.05)^10 = $ 162.89
To find the balance on an account after investing $100 at a 5% interest rate compounded annually for 10 years, you can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
Where:
A = the final account balance
P = the principal amount (initial investment)
r = the interest rate (in decimal form)
n = the number of times interest is compounded per year
t = the number of years
In this case, P = $100, r = 5% (or 0.05 as a decimal), n = 1 (since interest is compounded annually), and t = 10.
Substituting these values into the formula, we get:
A = $100(1 + 0.05/1)^(1*10)
A = $100(1 + 0.05)^10
A = $100(1.05)^10
To calculate this expression, we can use a calculator or a spreadsheet. Evaluating it, we find:
A ≈ $162.89
Therefore, the balance on the account after investing $100 at 5% interest compounded annually for 10 years would be approximately $162.89.