Business: Something something get free points something

Something something get free points something

raven82914

22.04.2021

Number of years = 7.54 or 8 years

Explanation:

We know,

YTM = $\frac{I + \frac{M - V_{o}}{n} }{\frac{2M + V_{o} }{3}}$

Here,

I = Coupon payment

M = Par value

V = Market price

Given,

M = Par value = $1,000

V = Market price = $1,119.34

I = Coupon Payment = Par value × Coupon rate = $1,000 × 6.4% = $64

Since, it is a semi-annual payment = $64/2 = $32

YTM = 4.6%

Therefore, putting the value into the above formula, we can get

YTM = $\frac{32 + \frac{1,000 - 1119.34}{n} }{\frac{(2*1,000) + 1,119.34}{3}}$

or, 0.046 = $\frac{\frac{32n - 119.34}{n} }{\frac{3,119.34}{3}}$

or, 0.046 = $\frac{\frac{32n - 119.34}{n} }{1,039.78}$

or, 47.82988 = $\frac{32n - 119.34}{n}$ [Multiplying both the sides by 1,039.78]

or, 47.82988n = 32n - 119.34 [Multiplying both the sides by n]

or, 47.82988n - 32n = -119.34

or, -15.82988n = -119.34

or, n = (-119.34) ÷ (-15.82988)

Therefore, n = 7.54 years or almost 8 years.

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