The problem asks us to calculate the yield to maturity (YTM) of a bond. We are given the following information: - Face Value = $1000 - Coupon Rate (CP) = 8% - Years to Maturity (Y) = 10 years - Current Price (P) = $750 - Coupon payments are made quarterly.

1. Problem Description

The problem asks us to calculate the yield to maturity (YTM) of a bond. We are given the following information:

- Face Value = $1000

- Coupon Rate (CP) = 8%

- Years to Maturity (Y) = 10 years

- Current Price (P) = $750

- Coupon payments are made quarterly.

2. Solution Steps

First, calculate the annual coupon payment:

Annual Coupon Payment = Face Value * Coupon Rate

$Annual Coupon Payment = 1000 * 0.08 = 80$

Since the coupon is paid quarterly, the quarterly coupon payment is:

$Quarterly Coupon Payment = Annual Coupon Payment / 4$

$Quarterly Coupon Payment = 80 / 4 = 20$

The number of periods is:

$Number of Periods = Years to Maturity * Number of Payments per Year$

$Number of Periods = 10 * 4 = 40$

Now, we need to estimate the Yield to Maturity (YTM). The approximate formula for YTM is:

$YTM = (Annual Coupon Payment + (Face Value - Current Price) / Years to Maturity) / ((Face Value + Current Price) / 2)$

$YTM = (80 + (1000 - 750) / 10) / ((1000 + 750) / 2)$

$YTM = (80 + 250 / 10) / (1750 / 2)$

$YTM = (80 + 25) / 875$

$YTM = 105 / 875$

$YTM = 0.12$

Since the coupon is paid quarterly, this YTM represents the quarterly YTM. To annualize, we need to multiply by the number of payments per year. Thus, we multiply 0.12 by

4.

$Annualized YTM = 0.12 * 4 = 0.48$

So, the approximate YTM is 48%.

A more precise calculation can be done using the following reasoning:

The quarterly discount rate r must satisfy the equation

$750 = 20 \sum_{k=1}^{40} \frac{1}{(1+r)^k} + \frac{1000}{(1+r)^{40}}$

This implies $750 = 20 \frac{1 - (1+r)^{-40}}{r} + \frac{1000}{(1+r)^{40}}$.

Solving for r is not trivial, but a rough approximation can be obtained through the method outlined above.

3. Final Answer

The approximate yield to maturity is 48%.