Bobbie Rae is lending Tommy Lee $4,500 to open up a bait shop at one of the nearby lakes. Tommy Lee says he will repay Bobbie Rae at the end of 4 years with 7% interest compounded quarterly. How much will Bobbie Rae receive at the end of the 4 years? Hint: Treat this like a one time investment problem.
To find out how much Bobbie Rae will receive at the end of the 4 years with 7% interest compounded quarterly, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount of money
P = the principal amount (initial investment)
r = annual interest rate (expressed as a decimal)
n = number of times the interest is compounded per year
t = number of years
In this case:
P = $4,500
r = 7% = 0.07 (expressed as a decimal)
n = 4 (compounded quarterly)
t = 4 years
Now, let's substitute these values into the formula:
A = 4500(1 + 0.07/4)^(4*4)
First, we need to simplify the term inside the parentheses:
1 + 0.07/4 = 1.0175
Now, let's continue simplifying the equation:
A = 4500(1.0175)^(16)
Using a calculator or a spreadsheet, we find:
A ≈ $5,497.78
Therefore, Bobbie Rae will receive approximately $5,497.78 at the end of the 4 years.