math question

Question

michelle needs to save $7,000 for school in the next two years. she found a bank that offers a 9% interest rate compounded annually. what does she need to desposit at the beginning of the year to have enough money for school?

Answer 1

9% for 2 yeers gro tu 1.09^2=1.1881

deposit rite now=7000$/1.1881

=0.84169993*7000

=5,891.76$

Answer 2

Let's call the amount she needs to invest P. After one year this would increase to P+9%P=P(1+9/100)=1.09P. After two years' compound interest this would increase to 1.09*1.09P=1.1881P. This amount needs to come to $7000, so 1.1881P=7000 and P=7000/1.1881=$5891.76.