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 and she puts it into an account that earns 4.25% interest compounded semi-annually. How much will be in kelly's account at the end of four years?
Austin plans to put her graduation money into an account earning compound interest and leave it there for four years. She receives $750 in graduation money and put it into an account that earns 4.25% interest compounded annually. How much will be in Austin’s account at the end of four years?
To calculate the amount that will be in Kelly's account at the end of four years, we can use the formula for compound interest:
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 = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
In this case:
P = $750
r = 4.25% = 0.0425 (as a decimal)
n = 2 (semi-annual compounding: 2 times per year)
t = 4 years
Substituting the values into the formula, we get:
A = $750(1 + 0.0425/2)^(2*4)
A = $750(1 + 0.02125)^8
A ≈ $750(1.02125)^8
A ≈ $750(1.186847)
A ≈ $891.63
So, at the end of four years, there will be approximately $891.63 in Kelly's account.
To find out how much will be in Kelly's account at the end of four years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount in the account
P = the principal amount (initial amount)
r = annual interest rate (expressed as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case, Kelly's principal amount (P) is $750, the interest rate (r) is 4.25% or 0.0425 (expressed as a decimal), the interest is compounded semi-annually (n = 2), and she plans to leave the money for 4 years (t = 4).
Now, substitute the given values into the formula:
A = 750(1 + 0.0425/2)^(2*4)
Start by simplifying the inside of the parentheses:
A = 750(1 + 0.02125)^(8)
Now, calculate the value inside the parentheses and raise it to the power of 8:
A = 750(1.02125)^(8)
Using a calculator, evaluate the expression inside the parentheses:
A = 750(1.185029229)
Multiply the principal amount by the calculated value:
A = 888.7729217
Therefore, at the end of four years, there will be approximately $888.77 in Kelly's account.
amount = principal(1i)^n
i = .0425/2 = .02125 , n = 8 , principal = 750
amount = 750(1.02125)^8 = 887.40