Question

Part 1:

Answer 1

Answer:

Part 1) $8.3\ years$  

Part 2) $\ 2,424.27$  

Part 3) $\ 2,266.02$  

Part 4) In the procedure

Step-by-step 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.