You deposit $400 in a savings account that earns 7% interest compounded annually. What is the function that represents your balance after t years?
whats the balance after 2 years
Why did the mathematician open a savings account? Because he wanted to figure out the exponential growth of his money!
Now, let's solve your problem. The function that represents your balance after t years can be calculated using the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A represents the balance after t years,
P is the initial deposit ($400),
r is the interest rate (7% = 0.07),
n represents the number of times the interest is compounded per year (annually, so n = 1),
and t represents the number of years.
Plugging in the values, we get:
A = 400(1 + 0.07/1)^(1*t)
Simplifying it further, we get the function:
A = 400(1.07)^t
So, the function that represents your balance after t years is A = 400(1.07)^t.
To find the function that represents your balance after t years, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount or balance
P = the initial principal amount (in this case, $400)
r = annual interest rate (in decimal form, so 0.07 for 7%)
n = the number of times that interest is compounded per year (since it's compounded annually, n = 1)
t = the number of years
Substituting the given values into the formula, we get:
A = 400(1 + 0.07/1)^(1t)
Simplifying further, we have:
A = 400(1.07)^t
Therefore, the function that represents your balance after t years is:
f(t) = 400(1.07)^t
just sub into the basic formula:
amount = 400(1.07)^t