Barry Newman's savings account has a balance of $2707. After 4 years, what will the amount of interest be at 5% compounded annually?
What is 2707(1.05)^4 - 2707 ?
To find the amount of interest earned on Barry Newman's savings account after 4 years at a 5% interest rate compounded annually, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount including interest
P = the principal amount (balance in the savings account)
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = number of years
In this case, the principal amount (P) is $2707, 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 4.
Plugging in these values into the formula, we have:
A = 2707(1 + 0.05/1)^(1*4)
Simplifying the exponent, we get:
A = 2707(1.05)^4
Using a calculator, we can find (1.05)^4 = 1.21550625. Multiplying this value by the principal amount:
A = 2707 * 1.21550625
A ≈ 3295.25
Therefore, the final amount including interest after 4 years will be approximately $3295.25. To find the amount of interest earned, we subtract the principal amount:
Interest = A - P
Interest = 3295.25 - 2707
Interest ≈ $588.25
So, the amount of interest earned on Barry Newman's savings account after 4 years at a 5% interest rate compounded annually is approximately $588.25.