You deposit $3350 into a savings account that earns 5% interest compounded annually. Find the balance of the account after 2 years. Round your answer to the nearest cent
What is 3350(1.05)^2 ?
$3693.38
To find the balance of the account after 2 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final balance
P = the principal amount (initial deposit)
r = the interest rate (in decimal form)
n = the number of times that interest is compounded per year
t = the number of years
Given:
P = $3350
r = 5% = 0.05
n = 1 (compounded annually)
t = 2
Plugging in the values into the formula, we can calculate the balance:
A = 3350(1 + 0.05/1)^(1*2)
Simplifying:
A = 3350(1.05)^2
A = 3350 * 1.1025
A ≈ $3698.13
Therefore, the balance of the account after 2 years would be approximately $3698.13
To find the balance of the account after 2 years, we need to calculate the amount of interest earned and add it to the initial deposit of $3350.
The formula to calculate compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (initial deposit)
r = annual interest rate (expressed as a decimal)
n = number of times that interest is compounded per year
t = number of years
In this case, the principal (P) is $3350, the annual interest rate (r) is 5% (or 0.05 as a decimal), the interest is compounded annually (n = 1), and the number of years (t) is 2.
Now we can substitute the values into the formula and calculate the balance:
A = 3350(1 + 0.05/1)^(1*2)
A = 3350(1 + 0.05)^2
A = 3350(1.05)^2
A = 3350(1.1025)
A = 3691.75
Therefore, the balance of the account after 2 years is approximately $3691.75.