Question

A $50 000, 11% bond with semi-annual coupons redeemable at par on April 15, 2022, was purchased on June 25, 2015, at 92.375. What was the approximate yield rate?

Answer 1

Answer -

In the given question redeemable value or par value of a bond is not given, but the purchase price of a bond is given as $92.375, hence the par value of a bond should be assumed as $100.

The bond was purchased on June 25, 2015 and redeemed on April 15, 2022

Now, for calculating the approximate yield rate, let us calculate the holding period of bond in days

Statement showing holding period of bond

Year	Number of Days
2015	190
2016	366
2017	365
2018	365
2019	365
2020	366
2021	365
2022	105
	2487

Now, let us calculate total interest paid by bond during holding period -

Total Interest = Face value * Coupon rate * Holding period

Where -

Face value is $100

Coupon rate is given as 11%

Holding period = 2487 days / 365 days

On putting these figures in the formula, we get -

Total Interest = Face value * Coupon rate * Holding period

Total Interest = $100 * 11% * (2487 days / 365 days)

Total Interest = $11 * (2487 days / 365 days)

Total Interest = $74.95 (approx)

Now, let us calculate the yield rate -

Yield = {(Redeemable value - Purchase price) + Total interest} / Purchase price

Where -

Redeemable value is $100

Purchase price is given as $92.375

Total interest calculated above as $74.95

On putting these figures in the formula, we get -

Yield = {(Redeemable value - Purchase price) + Total interest} / Purchase price

Yield = {($100 - $92.375) + $74.95} / $92.375

Yield = {$7.625 + $74.95} / $92.375

Yield = $82.575 / $92.375

Yield = 0.8939, or

Yield = 89.39% for 2487 days

Therefore,

Annual Yield = 89.39% * (365 days / 2487 days)

Annual Yield = 13.11%