Transcript Alison deposits $500 into a new savings account that earns 5 percent interest compounded annually.

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?
(a)
14
(b)
15
(c)
19
(d)
20
(e)
21
Correct Answer: B
Explanation:
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
500(1.05)n = 1000
follows.
1.05n = 2
n ln(1.05) = ln 2
n=
n = 14.2
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 xcoordinate of the point of intersection is approximately 14.2. Thus you need to round
up to 15.