Kelly plans to put her graduation money into an account and leave it there for 4 years while she goes to college. She receives $750 in graduation money that she puts it into an account that earns 4.25% interest compounded semi-annually. How much will be in Kellys account at the end of four years?
i = .0425/2 = .02125
n = 2(4) = 8
amount = principal(1+i)^n
= 750(1.02125)^8 = .....
To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/amount in the account after the given period
P = the principal amount (initial investment or starting amount)
r = annual interest rate (as a decimal)
n = number of times that interest is compounded per year
t = number of years
Let's apply this formula to the given information:
Principal amount (P) = $750
Annual interest rate (r) = 4.25% or 0.0425 (converted to decimal form)
Compounding frequency (n) = semi-annually (twice per year)
Number of years (t) = 4
Plugging in these values, we have:
A = 750(1 + 0.0425/2)^(2*4)
Now, let's calculate step by step:
A = 750(1 + 0.02125)^(8)
A = 750(1.02125)^(8)
A ≈ $857.45
Therefore, at the end of four years, there will be approximately $857.45 in Kelly's account.