Problem $7(22$ marks$)$

Tay and Trav $($T & T$)$ were recently engaged to be married and are planning their wedding. The couple plans to get married in two years and anticipates they will need $$2,000,000$

saved for their lavish wedding $($September $2026).$

a$.$ How much would T&T have to invest today to have $$2,000,000$ in $2$ years, if they can earn $8\%$ on their investments? $(2$ marks$)$

b$.$ Suppose they invested the amount calculated in $($a$),$ however can only earn $8\%$ simple interest. How much will they have accumulated $($in total$)$ for their wedding in $2$ years?

$(3$ marks$)$

c$.$ Calculate the rate of return $($compound interest$)$ T&T would have to earn over the next two years if they invest only $$1,500,000$ today if they want to have $$2,000,000$ saved.

$(2$ marks$)$

d$.$ Calculate how long it would take T&T to accumulate $$2,000,000$ if they invest $$1,600,000$ today and can earn $6\mathrm{.}5\%($compound interest$).(2$ marks$)$

e$.$ Instead of saving a lump sum today, T&T decide to make payments to their investment account every six months. Below are the cashflows and interest rates. How much will

they have accumulated at the end of $2$ years $($at time $4)?(6$ marks$)$