I plan to save $100,000$ won on January $1,1915,$ and $5,000$ won every day from the next day until December $31,1919.$ The annual interest rate is $5\%$ and interest is paid compounded daily.

$(1$ year $=365$ days, leap years are not considered.$)$

a$)$ Find the differential equation that satisfies when the value of the asset after t years is $($unit: $10,000$ won$).$

The answer is in the form dA$/$dt $=$ aA $+$ b $($A$(0)=$b$)$

b$)$ If you were to withdraw your savings on January $1,1920,$ how much would you receive?

c$)$ How many days later will the asset value exceed $3$ million won?