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 tenth

Solution:- As per Given Problem Principal = $1750Rate of interest (i) = 2.3 % =23/100 compounded annuallyRequired amount = $2400To find time =n (years)By using compound interest formula[tex]A=P(1+i)^n\\\text{we get,}\\\Rightarrow 2400=1750(1+\frac{2.3}{100})^n\\\Rightarrow\frac{2400}{1750}=(1+0.023)^n\\\Rightarrow1.3714=(1.023)^n\\\text{taking log on both sides,we get}\\log(1.3714)=log((1.023)^n)\\\Rightarrow0.3158=n(log(1.023))\\\Rightarrow0.3158=n(0.0227)\\\Rightarrow\ n=13.911\approx 14[/tex]So, it will take around 14 years to earn enough money to go on the trip.