Question

A $180,000 issue of seven-year bonds redeemable at par offers 6.24% coupons payable monthly. What is the premium or discount and the purchase price of the bonds to yield 9.6% compounded annually?

ANSWERS GIVEN

a) The DISCOUNT is $27,436.49

b) The purchase price of the bond is $152,563.51

**Note: would like to know how to get to these answers. Using a TI BA II PLUS. Please show Calculator solution (Easiest solution). Thank you *

Answer 1

YTM = 9.6% annually

APR(monthly) = 12[(1 + 0.096)1/12 - 1]

APR(monthly) = 9.202%

Par Value = $180,000

Coupon Payment = 180,000(0.0624/12) = $936

Time Period = 84 months

Calculating Bond Price,

Using TVM Calculation,

PV = [FV = 180,000, PMT = 936, N = 84, I = 0.09202/12]

PV = $152,563.51

Bond Price = $152,563.51

DIscount = 180,000 - 152,563.51

Discount = $27,436.49

Answer 2

Step-by-Step Calculation (Using TI BA II Plus):

1. Input Given Data:

• Face Value (FV): $180,000

• Coupon Rate: 6.24% annually → Monthly Coupon Payment:

  $$\text{PMT}=\frac{6.24\mathrm{\%}\times \mathrm{\$}180,000}{12}=\mathrm{\$}936$$

• Time to Maturity (N): 7 years → 84 months (7 × 12)

• Yield (YTM): 9.6% compounded annually → Monthly Equivalent Rate:

  $$(1+0.096{)}^{1\mathrm{/}12}-1=0.767\mathrm{\%}\text{ per month}$$

2. Calculate the Purchase Price (PV):

• Set Calculator to END Mode:

• 2nd → PMT → 2nd → ENTER (to toggle BGN/END).

• Input:

• N = 84

• I/Y = 0.767 (monthly rate)

• PMT = 936

• FV = 180,000

• CPT → PV

Result:

$$PV=-\mathrm{\$}152,563.51(\text{Price paid})$$

3. Calculate the Discount:

$$\text{Discount}=\text{Face Value}-\text{Purchase Price}=\mathrm{\$}180,000-\mathrm{\$}152,563.51=\mathrm{\$}27,436.49$$

Answer:
The bond has a discount of $27,436.49\ast \ast anda\ast \ast purchasepriceof$