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 $$2,000,0000$ if they invest $$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$)$

f$)$ Instead of saving a lump sum today, T&T decide to save the same amount each month for the next two years to accumulate the $$2,000,000$ they need for the wedding. If they can earn $0\mathrm{.}75\%(0\mathrm{.}0075)$ per month, calculate the mlnthly deposit required at the end of each month. $(5$ marks$)$

g$)$ How would your answer to $($f$)$ change of they make their deposits at the start of each month.$(2$ marks$)$