Question $8$

Afifah can buy one of two following bonds:$-$

Bond $1$: a zero coupon bond that will pay RM$1,500$ at the end of $10$ years.

Bond $2$: a $5\%$ bond coupon rates payable semi$-$annually based on RM$1,000$ face

value, that will pay RM$1,000$ at the end of $10$ years. The coupons are then re$-$

invested at the nominal rate of $4\%$ convertible semi$-$annually.

Bond $1$ and Bond $2$ are currently sold at RM$837\mathrm{.}59$ and RM$850$ respectively.

$($a$)$ For Bond $1,$ find the effective rate of return for the zero coupon bond if she

wishes to purchase it$.$

$($b$)$ For Bond $2,$ Afifah determines $RMx$ as the price of the bond using the

same rate of return as in Bond $1.$

$($i$)$ Calculate the future value of Bond $2$ under the nominal re$-$invested

rate of $4\%$ convertible semi$-$annually, at the end of $10$ years.

$($ii$)$ By using the effective rate of interest under Bond $1,$ calculate $x.$

$($c$)$ Choose which one of the two following bonds is better. State the reason.