An amount of $5000 is invested at an interest rate of 7% per year, compounded quarterly.
Find the value A(t) of the investment after t years.
A(t) = Ao(r + 1)^n.
r = (7/4) / 100 = 0.0175 = Quarterly
percentage rate(QPR).
n = 4 comp / yr * t yrs = 4t.
t = Time for maturity or withdrawal in years.
A(t) = 5000(1.0175)^4t.
A(5) = 7073.89.
A(8) = 8711.07.
To find the value A(t) of the investment after t years, you can use the formula for compound interest:
A(t) = P(1 + r/n)^(nt)
Where:
- A(t) is the value of the investment after t years
- P is the principal amount (initial investment), which is $5000 in this case
- r is the interest rate per year, expressed as a decimal, which is 7% or 0.07
- n is the number of times interest is compounded per year, which is quarterly (4 times in a year)
- t is the number of years
To find the value of A(t), we substitute the given values into the formula:
A(t) = 5000(1 + 0.07/4)^(4t)
Simplifying further,
A(t) = 5000(1 + 0.0175)^(4t)
Now you can calculate the value of A(t) by substituting the value of t for the desired number of years.