Question

Amortization: Consider a 4‐year bond with face value of 100 and an

annual coupon rate of 5%. Calculate the annual payments and outstanding principal for

three kinds of bonds (in terms of principal repayment). A) A bullet bond. B) A fully

amortizing bond. C) A partially amortizing bond with a balloon principal payment of $30 at

the end.

Answer 1

A) Bullet bond

Coupon rate = 5%

Face value = 100

Annual payments = 5%*100 = $5

Outstanding principal = $100

B) A fully amortizing bond

A: amount = 100

t: time = 4years

r: interest rate = 5%

P: annual emi

A = (P/r)*(1-1/(1+r)^t)

100 = (P/5%)*(1-1/(1+5%)^4)

P = 28.20

Annual payments = $28.20

Outstanding principal = 0

Partially amortizing bond

A: amount = 100

t: time = 4years

r: interest rate = 5%

X: annual emi

ballloon principal payment = 30

A = (X/r)*(1-1/(1+r)^t)+30/(1+r)^t

100 = (X/5%)*(1-1/(1+5%)^4)+30/(1+5%)^4

X = 21.24

Annual payments = $21.24

Outstanding principal = $30