Question

You and your best friend want to backpack through Europe. You have done some research and discovered that it will cost $2,000 for the plane ticket, rail pass, food, and lodging. You have already saved $1,500. If you invest this money in a savings account with a 3% interest rate compounded annually, how long will it take to earn enough money to go on the trip? Use the compound interest formula A = P (1 + i)n, where A is the accumulated amount, P is the principal, i is the interest rate per year, and n is the number of years.

I believe that the formula is 2,000=1,500(1+0.03)^n

Answer 1

I know the answer is 9.7 but I don't know how to get to there.

Answer 2

2,000=1,500(1+.03)^n
/1,500 /1,500
4/3=(1+.03)^n
4/3=1.03^n
\[\ln_{1.03} \frac{ 4 }{ 3 }= n \]
\[\frac{ \ln \frac{ 4 }{ 3 } }{ \ln 1.03 }\]

Answer 3

or guess and check

Answer 4

you have the equation correct,

so all that is left is to 'isolate' n
what part of isolating n doesn' make sense?

Answer 5

ahh okay, this is how I got it 2,000=1,500(1+0.03)^n
2000/1,500=1.33333333 = 1(1.03)^n
log (1.333)/log(1.03) = 9.73 or 9.7

Answer 6

good, ya

Answer 7

thankss again :)

Answer 8

and thank you @yomylola :)