An investor is proposed to invest $RM48,000$ and is promised in return of annual

payment series of RM$4,500$ paid at the end of each year for the first $10$ years, and

another annual payment series of RM$5,000$ paid at the end of each year for the

next $10$ years.

$($a$)$ Using the effective interest rate of $i,$ construct the Net Present Value $($NPV$)$

of the payments above.

$($b$)$ For $i=6\%,7\%,8\%,$ find the respective NPVs$.$

$($c$)$ If the proposed present value is the invested amount of RM$48,000,$ by

using interpolation obtained by $($b$),$ find his internal rate of return $($IRR$).$