An investment pays 8% interest, compounded annualy.
Write an ewuatiin that expressed the amount A, of the investment as a function of time, t, in years
A = P(1.08)^t
where P is the initial investment or "principle"
If t is not an integer number of years, the next lower integer must be used, since interest is only compunded at the end of a year in this example. Some banks and bond transfer agents will credit partial-year interest up to the time of withdrawal, however.
To express the amount A of an investment as a function of time t, with 8% interest compounded annually, we can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
Where:
A is the amount of the investment after time t
P is the principal amount (initial investment)
r is the annual interest rate (expressed as a decimal, so 8% would be 0.08)
n is the number of times interest is compounded per year
t is the time in years
In this case, the interest is compounded annually, so n = 1. The equation becomes:
A = P(1 + 0.08/1)^(1*t)
Simplifying it further, we get:
A = P(1.08)^t
Therefore, the equation expressing the amount A of the investment as a function of time t is:
A = P(1.08)^t