Exercise 1.3.66

Question

If you invest $x$ dollars at $4 \%$ interest compounded annually, then the amount $A(x)$ of the investment after one year is $A(x)=1.04 x$. Find $A \circ A, A \circ A \circ A$, and $A \circ A \circ A \circ A$. What do these compositions represent? Find a formula for the composition of $n$ copies of $A$.

Khagan Gulusoy · Accepted Answer

$$
\begin{aligned}
& A \circ A(x)=A(A(x))=A(1.04 x)=1.04^{2} x . \
& A \circ A \circ A(x)=1.04^{3} x .\
&A \circ A \circ A \circ A(x)=1.04^{4} x.\
&\underbrace{A\circ A\circ A\circ \ldots(x)}_{n 	ext { times }}=1.04^{n} x 	ext {. }\end{aligned}$$
The compositions represent the amount of the investment after 2 years, 3 years, and $4$ years after investing $x$ dollars.

Exercise 1.3.66

Answers

Comments

Exercise 1.3.66

Answers

Comments

Add answer