amount = principal(1i)^n
i = .0425/2 = .02125 , n = 8 , principal = 750
amount = 750(1.02125)^8 = 887.40
i = .0425/2 = .02125 , n = 8 , principal = 750
amount = 750(1.02125)^8 = 887.40
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 β $750(1.02125)^8
A β $750(1.186847)
A β $891.63
So, at the end of four years, there will be approximately $891.63 in Kelly's account.
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.