Subject Test Math 2

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Subject Test Math 2

Question 4 of 28

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Alison deposits $$ 500$ into a new savings account that earns $5$ percent interest compounded annually. If Alison makes no additional deposits or withdrawals, how many years will it take for the amount in the account to double?

Select an Answer

$14$

Correct Answer:

No

$15$

Correct Answer:

Yes

$19$

Correct Answer:

No

$20$

Correct Answer:

No

$21$

Correct Answer:

No

View Correct Answer

After $1$ year, the amount in the account is equal to $$ 500 (1.05)$ . After $2$ years, the amount is equal to ${$ 500 (1.05)}^{2}$ , and so on. After $n$ years, the amount is equal to $$ 500 {(1.05)}^{n}$ . You need to find the value of $n$ for which $500 {(1.05)}^{n} = 1000$ . There are several ways to solve this equation. You can use logarithms to solve the equation as follows.

Since $n = 14.2$ , it will take more than $14$ years for the amount in the account to double. Thus, you need to round $14.2$ up to $15$ .

Another way to find $n$ is to use your graphing calculator to graph $y = 500 {(1.05)}^{x}$ and $y = 1000$ . From the answer choices, you know you need to set the viewing window with $x$ values from $0$ to about $25$ and $y$ values extending just beyond $1000$ . The $x -coordinate$ of the point of intersection is approximately $14.2$ . Thus you need to round up to $15$ .