A savings account with a current balance of $5,000 earns 2.75% annual interest,
compounded continuously. To the nearest dollar, what will be the account balance in 10
years?
5000(1+0.0275*10)
=6375
To find the account balance in 10 years, we can use the formula for continuously compounded interest:
A = P * e^(rt)
Where:
A is the account balance after time t
P is the principal amount (initial balance)
e is the mathematical constant approximately equal to 2.71828
r is the annual interest rate (in decimal form)
t is the time period in years
In this case, the initial balance (P) is $5,000, the annual interest rate (r) is 2.75% or 0.0275 (expressed as a decimal), and the time period (t) is 10 years.
Let's plug in these values into the formula:
A = 5000 * (2.71828)^(0.0275 * 10)
Using a calculator, we can calculate:
A ≈ 5000 * (2.71828)^(0.275)
A ≈ 5000 * 1.316811
A ≈ 6584.055
Rounding to the nearest dollar, the account balance after 10 years will be approximately $6,584.