Question

Assume that a partially amortized 10-year and 5% coupon semi-annual bond has a balloon payment of $500. The total amount of the principal reimbursed after 18 months is closest to: A 20.56 B 60.19 C 61.68

Answer 1

The bond has a balloon payment of 500 at the end of 10 year.

The bond pays 5% coupon semi-annually, hence, half-yearly coupon rate is 5%/2 = 2.5%

Since coupon is paid semi-annually, hence, the number of time periods becomes 10 * 2 = 20

Now, calculating Present Value of Balloon payment at Period 0 and Period 3 (18 months).

PV of Balloon Payment at Period 0 = 500 / (1+2.5%)²⁰ = 500 / 1.638616 = 305.14

PV of Balloon Payment at Period 3 (18 months) = 500 / (1+2.5%)¹⁷ = 500 / 1.521618 = 328.60

Amount of principal reimbursed after 18 months = PV of Balloon Payment at 18 months - PV of Balloon Payment at Period 0 = 328.60 - 305.14 = 23.46

Hence, answer is A as 23.46 is closest to 20.56.