Exercise $2\mathrm{.}7$: I invest money in a savings account that pays a nominal interest of $6\%$ p$.$a$.$ compounded monthly. I open the account with a deposit of $$1000$ and then deposit $$50$ at the end of each month for a period of two years followed by a monthly deposit of $$100$ for the following $3$ years. What will be the value of my savings account at the end of the five$-$year period?