# Finance Mathematics: Design a Budget

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Leslie earns $2000 a month and rents an apartment for $600 a month (utilities included), and also has a credit card with an annual interest rate of 7% and a balance of $1500. She currently has no savings. Design a monthly budget for Leslie so that at the end of two years, the credit card balance is as low as possible and Leslie has as much savings as possible. (You may assume that if she opens a savings account, it draws 3% annual interest compounded monthly.) Remember that Leslie needs to use some money for food and miscellaneous expenses.

Assuming that she sticks to the budget you design, what will he credit card balance be at the end of two years, and how much will she have in savings?

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##### Solution Summary

A budget is designed under given constriants. The solution is detailed and well explained.

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Leslie earns $2000 a month and spends $600 a month for the rent. So her net earning is $2000-$600=$1400. Each month, she pays x dollars for the credit card and save y dollars in her saving account. Since she needs to use some money for food and miscellaneous expenses, x+y<1400. The credit card has an annual interest rate of 7%, so the monthly rate is 7%/12=0.07/12.

After 1 month, the balance of the credit card is ...

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