Question

In preparation to buy a new video game that cost $65, your friend plans on saving money each month for the purchase of the game. Your friend initially starts her savings with $10 in January, and plans on saving 10% more during each successive month. After what month will your friend be able to purchase the video game?

Answer 1

After 20 months

Explanation:

This is a compound growth problem which has the formula:

`F=P(1+r)^t`

Where

F is future value

P is present amount

r is the rate of growth

t is the time (in months)

Future amount is $65, what he needs at-least

P is the initial amount, that is $10

r is the rate of growth, which is 10% or 10/100 = 0.1

t is time in months, what we need to find

Substituting and solving we get:

`F=P(1+r)^t\\65=10(1+0.1)^t\\65=10(1.1)^t\\6.5=1.1^t\\ln(6.5)=ln(1.1^t)\\ln(6.5)=t*ln(1.1)\\t=(ln(6.5))/(ln(1.1))\\t=19.64`

He would need 19.64 months to save up at-least 65. So, that means, he would need 20 months