You have a savings goal to purchase a house in $5$ years. However, you want minimize your

mortgage payments as much as possible. You decide to set a lofty goal to put down $$100,000$

when its time to purchase. To achieve this, you plan to make a one$-$time lump sum investment

now and let it grow over the $5-$year period. The bank offers a special plan for first time home

buyers that offers an annual interest rate of $8\%,$ with the interest being compounded monthly.

What initial lump sum amount do you need to invest today to ensure that your investment

grows to $$100,000$ in $5$ years? $($round to the nearest dollar$)$ $