A loan of $RM200,000,$ paid annually, is made for a term of $30$ years at an effective interest

rate of $4\mathrm{.}5\%.$ The lender allows only annual year$-$end interest payments made until at the end

of $30$ years. In order to pay the loan of $RM200,000$ at the end of $30$ years, the borrower will

make a payment of $R$ at the end of first year, and will increase his payments of $R$ arithmetically

for the subsequent years, into a sinking fund earning $6\%$ interest rate per year.

$($a$)$ Develop a sales illustration of this loan scheme which consists of the following:$-$

$($i$)$ Part $1$:$-$ parameters of input $($loan$,$ loan interest rate, loan period, rate of

investment return$).$

$($ii$)$ Part $2$:$-$ output $-$ table schedule which consists of sinking fund deposit, total

sinking fund deposit, sinking fund interest, principal repayment in sinking fund

and outstanding balance of the loan.

$($b$)$ From $($a$)($ii$),$ determine,

$($i$),R.$

$($ii$)$ Total principal repayment for the $10-$th payment.

$($iii$)$ The total profit of the borrower taking under this scheme for $30$ years period.

$($c$)$ Submit the report of this illustration by the following:$-$

$($i$)$ Written answer $($in pdf files$)-$ develop suitable formula and payment schedule

to answer $($b$)$

$($ii$)$ Sales illustration $($in MSExcel$)-$ to answer $($b$)$