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Part 1:
You and your best friend want to take a vacation to Australia. You have done some research and discovered that it will cost $2500 for the plane tickets, all-inclusive hotel and resort, and souvenirs. You have already saved $2200. If you invest this money in a savings account with a 1.55% 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 tenth






Part 2:
You are planning to go on this trip in 2 years. How much money will you need to invest at a 1.55% interest rate compounded annually in order to have $2500 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)







Part 3:
Now say you only have $2000 to invest and the highest interest rate you can find is 1.8% 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)





Part 4:
Write a paragraph explaining how you would prepare financially for this trip. Would you invest the $2200 and wait until it grows to $2500? Would you add to the investment of $2200 so it will grow to $2500 by the time you want to take the trip? Would you invest the $2200 and come up with the rest of the money when you want to take the trip? Explain your answer.

Respuesta :

calculista

Answer:

Part 1) [tex]8.3\ years[/tex]  

Part 2) [tex]\$2,424.27[/tex]  

Part 3) [tex]\$2,266.02[/tex]  

Part 4) In the procedure

Step-by-step explanation:

Part 1) we know that    

The compound interest formula is equal to  

[tex]A=P(1+i)^{n}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

i is the interest  rate  in decimal

n is number of years  

n is the number of times interest is compounded per year

in this problem we have  

[tex]P=\$2,200\\ A=\$2,500\\ r=0.0155\\n=?[/tex]  

substitute in the formula above  

[tex]\$2,500=\$2,200(1+0.0155)^{n}[/tex]  

[tex](2,500/2,200)=(1.0155)^{n}[/tex]  

Applying log both sides

[tex]log(2,500/2,200)=(n)log(1.0155)[/tex]  

[tex]n=log(2,500/2,200)/log(1.0155)[/tex]

[tex]n=8.3\ years[/tex]  

Part 2)

in this problem we have  

[tex]P=?\\ A=\$2,500\\ r=0.0155\\n=2\ years[/tex]  

substitute in the formula above  

[tex]\$2,500=P(1+0.0155)^{2}[/tex]  

[tex]\$2,500=P(1.0155)^{2}[/tex]  

[tex]P=\$2,500/(1.0155)^{2}[/tex]  

[tex]P=\$2,424.27[/tex]  

Part 3) in this problem we have  

[tex]P=\$2,000\\ r=0.018\\n=7\ years[/tex]  

substitute in the formula above  

[tex]P=\$2,000(1+0.018)^{7}=\$2,266.02[/tex]  

The money is not enough

Part 4)

I would personally increase the investment from 2,200 dollars so that it grows to 2,500 dollars at the time I want to make the trip, for example if I wanted to make the trip in two years, I would increase the initial investment from 2200 dollars to 2427 dollars.