Question

Today, stacy is investing $18,000 at 6.72 percent, compounded annually, for 5 years. how much additional income could she earn if she had invested this amount at 7.15 percent, compounded annually?

Answer 1

If x is the interest rate, we have that after 1 year Stacy gets a return of 18000*(1+x).After another year, this new sum needs to be multiplied again by (1+x). Thus, inductively one sees that after n years of annual compounding, Stacy will have returns 18000*[(1+x)^n] and the general formula for any initial capital C is: C*[(1+x)^n]. In the first case the interest rate is 6,72%, so x=0,0672 and in the second case x=0,0715. Substituting these numbers (and n=5 years) we get that in the first case (6,72%) Stacy gets 24917,33$ and in the second case (7,15%) she gets 25423,39$. The difference of these sums is the income that Stacy could have earned. This difference is equal to 506,06$