Chapter 5.4, Problem 2E

Round all answers to two decimal places unless otherwise indicated.

Investment Balance You invest $B_0$ dollars in an account that draws interest at a monthly rate of $r$ as a decimal, compounded monthly. After $t$ months, the balance in dollars is given by

$B=B_0{\left(1+r\right)}^t$.

a. Let $a$ denote the APR as a decimal. Then the monthly rate as a decimal is equal to $a$ divided by $12$. Express the balance in terms of initial investment, the number of months, and the APR as a decimal.

b. Let $a$ denote the APR as a decimal, and let $A$ denote the APR as a percentage. Then $a$ is equal to $A$ divided by $100$. Express the balance in terms of initial investment, the number of months, and the APR as a percentage.

c. Note that $y$ years is equivalent to $12y$ months. Express the balance in terms of the initial investment, the number $y$ of years, and the APR as a percentage.