Question

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.

Answer 1

Part 1)
`8.3\ years`

Part 2)
`\$2,424.27`

Part 3)
`\$2,266.02`

Part 4) In the procedure

Explanation:

Part 1) we know that

The compound interest formula is equal to

`A=P(1+i)^(n)`

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

`P=\$2,200\\ A=\$2,500\\ r=0.0155\\n=?`

substitute in the formula above

`\$2,500=\$2,200(1+0.0155)^(n)`

`(2,500/2,200)=(1.0155)^(n)`

Applying log both sides

`log(2,500/2,200)=(n)log(1.0155)`

`n=log(2,500/2,200)/log(1.0155)`

`n=8.3\ years`

Part 2)

in this problem we have

`P=?\\ A=\$2,500\\ r=0.0155\\n=2\ years`

substitute in the formula above

`\$2,500=P(1+0.0155)^(2)`

`\$2,500=P(1.0155)^(2)`

`P=\$2,500/(1.0155)^(2)`

`P=\$2,424.27`

Part 3) in this problem we have

`P=\$2,000\\ r=0.018\\n=7\ years`

substitute in the formula above

`P=\$2,000(1+0.018)^(7)=\$2,266.02`

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.