Fei wants to buy a new house, but does not have enough money for the down payment $($DP$).$

When she does buy a house she will purchase one that costs $$250,000.$ Thus, the amount she

needs to borrow will be $$250,000-$ DP$.$ She will borrow this money for $30$ years at an interest

rate of $0\mathrm{.}5\%$ per month compounded monthly.

Fei will save $$1250$ per month starting in one month $($period $1)$ for her down payment. She will

place this money in savings account that earns $0\mathrm{.}5\%$ interest each month per month

compounded monthly$).$

How long will Fei have to save such that her monthly house payment will also be $$1250$ per

month?

Make sure to draw any cash flow diagrams that you need.