Question

Suppose that 1500 is invested at 9% interest compound quarterly. Find the function for the amount of money after T years.

A(t)=

Answer 1

The formula for the amount of money A after T years with an initial investment P and a quarterly interest rate r, compounded n times per year is:

A = P(1 + r/n)^(nT)

In this case, P = 1500, r = 9%, n = 4 (quarterly compounding), so the formula becomes:

A(T) = 1500(1 + 0.09/4)^(4T)

Simplifying and rounding to two decimal places, we get:

A(T) = 1500(1.0225)^(4T)