You deposit $3000 in an account earning 5% interest compounded monthly. How much will you have in the account in 10 years?
To calculate the amount in the account after 10 years, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount in the account
P = the initial deposit
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
In this case:
P = $3000
r = 5% = 0.05
n = 12 (compounded monthly)
t = 10 years
Substituting these values into the formula:
A = 3000(1 + 0.05/12)^(12*10)
Simplifying:
A = 3000(1.0041667)^(120)
A ≈ 3000(1.6487212707)
Calculating:
A ≈ $3000 * 1.6487212707
A ≈ $4946.16
Therefore, you will have approximately $4946.16 in the account after 10 years.