Please help with these Algebra II word problems
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Please help with these Algebra II word problems

[From: ] [author: ] [Date: 12-07-12] [Hit: ]
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?......
Part 1:
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.




Part 2:
You are planning to go on the trip to Europe in 2 years. How much money will you need to invest at a 3% interest rate compounded annually in order to have $2000 in 2 years? Use the compound interest formula A = P (1 + i)n.




Part 3:
You only have $1500 to invest and the highest interest rate you can find is 3% compounded annually. If you decide to wait 4 years to go on the trip, how much money will you have to spend on the trip? Use the compound interest formula A = P (1 + i)n.

Thanks in advance!

-
Lexi

Part 1:
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.


1500(1+.03)^n = 2000

(1.03)^n = 1.3333, now use property of logs ...

nlog(1.03) = log 1.3333

n = log 1.3333 / log 1.03 = 9.7 years



Part 2:
You are planning to go on the trip to Europe in 2 years. How much money will you need to invest at a 3% interest rate compounded annually in order to have $2000 in 2 years? Use the compound interest formula A = P (1 + i)n.


P(1.03)^2 = 2000

P = 2000 / (1.03)^2 = 1885.19



Part 3:
You only have $1500 to invest and the highest interest rate you can find is 3% compounded annually. If you decide to wait 4 years to go on the trip, how much money will you have to spend on the trip? Use the compound interest formula A = P (1 + i)n.


1500(1.03)^4 = 1688.26

Hope that helps
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