If you can show your work so I can learn that would be great (all three questions go together). If you have any questions please ask1. You and your best friend want to take a vacation to Peru. You have done some research and discovered that it will cost $2400 for the plane tickets, all-inclusive hotel and resort, and souvenirs. You have already saved $1750. If you invest this money in a savings account with a 2.3% 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. Round your final answer to the nearest tenth2. You are planning to go on this trip in 2 years. How much money will you need to invest at a 2.3% interest rate compounded annually in order to have $2400 in 2 years? Use the compound interest formula A = P (1 + i)n. (Round final answer to the nearest cent, but otherwise don’t round any intermediate values)3. Now say you only have $1600 to invest and the highest interest rate you can find is 3.55% compounded annually. If you decide to wait 7 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. (Round final answer to the nearest cent, but otherwise don’t round any intermediate values)
Accepted Solution
A:
1) 13.9 years 2) $2293.30 3) $2042.54
Explanation: 1) Using the equation [tex]A=p(1+i)^n[/tex], plugging in our values, we have:
Using logarithms to solve this, we have: [tex]\log_{1.023}(\frac{2400}{1750})=n
\\
\\13.9=n[/tex]
2) This time, we substitute different values into our equation: [tex]A=p(1+i)^n
\\
\\2400=p(1+0.023)^2
\\
\\2400=p(1.023)^2
\\
\\\frac{2400}{1.023^2}=p
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\\2293.30 = p[/tex]
3) This time we change all of the values in our equation: [tex]A=p(1+i)^n
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\\A=1600(1+0.035)^7
\\
\\A=1600(1.035)^7
\\
\\A=2042.54[/tex]