Question

both questions are together

If you buy and hold full-term a 30-year bond that pays $70 semi-annually, what compound rate of return will you earn if you do not re-invest the coupon stream? 7% 7.5% 8.57% 2.79%. 5.57%

What rate of return did you earn if instead you reinvested at an annual rate of 6% semi-annually compounded? 8.57% 14% 7% 8%.

Answer 1

1. Assumed Principal Amount = $1000

Interest amount (semi-annually) = $70

Period = 30 years

Total Interest Amount = $70 x 30 x 2 (per year) = $4200

Total proceeds at the end of 30 years = Principal + Interest = $1000 + $4200 = $5200

Compound Interest equation is as following :

A = P(1 + r/n)^nt

Where:

A = Accrued Amount (principal + interest)

P = Principal Amount

I = Interest Amount

r = Annual Nominal Interest Rate as a decimal

t = Time Involved in years, 0.5 years is calculated as 6 months, etc.

n = number of compounding periods per unit t; at the END of each period

$5200 = $1000 (1+r/60)⁶⁰

r = 60 x [5.2^1/60-1]

On solving, we will get r = 5.57%

So, the correct answer is 5.57%

2. Under this, $70 shall be reinvested at the annual rate of 6% semi-annually.

So, the compound interest received at the end of 30 years shall be as following:

Total Interest = 70(1+0.03) + 70(1+0.03)² + 70(1+0.03)³ + ……….. + 70(1+0.03)⁶⁰= $11,343.73

Total proceeds at the end of 30 years = Principal + Interest = $1000 + $11,343.73= $12,343.73

Compound Interest equation is as following :

A = P(1 + r/n)^nt

Where:

A = Accrued Amount (principal + interest)

P = Principal Amount

I = Interest Amount

r = Annual Nominal Interest Rate as a decimal

t = Time Involved in years, 0.5 years is calculated as 6 months, etc.

n = number of compounding periods per unit t; at the END of each period

$12,343.73 = $1000 (1+r/60)⁶⁰

r = 60 x [12.344^1/60-1]

On solving, we will get r = 8.57%

So, the correct answer is 8.57%