  ### Home > INT2 > Chapter 9 > Lesson 9.3.2 > Problem9-95

9-95.

Mateo is saving money for college. He put $\1000$ in a no‑interest, no fees checking account. At the end of each year his grandparents give him $\200$ to add to the account. Mateo’s friend Marcy has saved $\1000$, and she put this money into an investment that earns $8\%$ annual interest. At the end of each year, Marcy pays an investment management fee of $\15$ and she adds $\100$ to the account from her babysitting earnings.

1. Make a table showing how much money Mateo and Marcy will have in their accounts at the end of each year for the first five years. Start your table with Year $0$.

 Year Mateo $(\)$ Marcy $(\)$ $0$ $1000$ $1000$ $1$ $1200$ $1165.00$ $2$ $1400$ $1343.20$ $3$ $1600$ $1535.66$ $4$ $1800$ $1743.51$ $5$ $2000$ $1967.99$

1. What was the average rate of change of each account from Year $0$ to Year $2$? Show your work and include units in your answers.

$\frac{\text{(money at year 2)-(money at year 0)}}{2-0}$

2. What was the average rate of change from Year $3$ to Year $5$ in each account?

Refer to part (b).

3. Whose account will have more money in the long run? Explain using your results from part (b) and part (c).

Does linear or exponential grow faster in the long run?