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Michelle is attending college and has a​ part-time job. Once she finishes​ college, Michelle would like to relocate to a metropolitan area. She wants to build her savings so that she will have a​ "nest egg" to start her off. Michelle works out her budget and decides she can afford to set aside ​$ per month for savings. Her bank will pay her per​ year, compounded​ monthly, on her savings account. What will be​ Michelle's balance in five​ years?

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Answer: $3,232.34

Explanation:

Michelle is depositing a constant amount so this is an annuity. The balance on her account will be the future value of an annuity.

5 years to months = 5 * 12 = 60 months

3% to monthly rate = 3%/12 = 0.25%

Future value of annuity

[tex]=Payment * \frac{(1 + r)^{n} - 1 }{r} \\=50 * \frac{(1 + 0.0025)^{60} - 1 }{0.0025}\\= 3,232.34[/tex]

= $3,232.34

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