$($a$)$ A loan of RM$30000$ is to be repaid by year$-$end level payments for $25$ years and

calculated on the basis of an interest rate of $12\%$ per annum.

$($i$)$ Calculate the annual payment

$($ii$)$ Calculate the capital payment and interest paid at the end of tenth year.

$($iii$)$ Determine after which payment the outstanding loan will first be less than

RM$18000$

$($iv$)$ Determine which payment the capital content will first exceed the interest

content.

$($b$)$ Donald takes out a loan of RM$30000$ for $10$ years with interest charged at $8\%$

convertible quarterly. Donald replaces two$-$fifth of the principal in a sinking fund

earning $5\%$ convertible semi$-$annually and the remaining three$-$fifth in a sinking

fund earning $7\%$ convertible semi$-$annually. Interest on the loan and deposits on

both sinking funds are made semi$-$annually. Calculate the total semi$-$annual

payment made by Donald.