Find the balance on an account if you invest $100 at 5% for 10 years compounded monthly.
.05/12 = .004166667
100 ( 1.004166667)^120
= $164.70
To find the balance on the account after investing $100 at a 5% interest rate compounded monthly for 10 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final account balance
P = the principal amount (initial investment)
r = the annual interest rate (written as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
In this case:
P = $100
r = 5% = 0.05 (converted to decimal)
n = 12 (monthly compounding)
t = 10 years
Plugging these values into the formula, we get:
A = 100(1 + 0.05/12)^(12*10)
Now, let's calculate the balance:
A = 100(1 + 0.00416667)^(120)
A = 100(1.00416667)^(120)
A ≈ 100(1.647009)
A ≈ $164.70
Therefore, the balance on the account after investing $100 at 5% interest for 10 years compounded monthly would be approximately $164.70.