Question

Please show all work

Yield to maturity. (a) Find the yield to maturity on a 1-month T-bill with $100,000 face value that sold for a price of $99,667.77.

Answer: i = 0.04

(b) Consider a loan of $400,000 to be repaid with annual payments over 25 years. Find the fixed payments that would be required for the yield to maturity on the loan to be 6%.

Answer: FP = $31,290.68.

(c) Consider a loan of $200,000 to be repaid with annual payments over 30 years. If the annual fixed payments are $19,467.28, then what is the yield to maturity on the loan? Show your work.

Answer: i = 0.09

Answer 1

Calculate the yield to maturity as follows:

Yield to maturity = ((Face value - Issue price) / Face value))*Number of months in a year

Yield to maturity = (($100,000 - $99667.77) / $100,000)) *12

Yield to maturity = 0.04 or 4%

i = 0.04.

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b.

Calculate the payment as follows:

Payment = Present value *Rate) / (1-(1+rate)^-number of years))

Payment = ($400,000*6%) / (1-(1+6%)^-25))

Payment = $24,000 / 0.767

Payment = $31,290.69.

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c.

Calculate the yield to maturity as follows:

Payment = Present value *Rate) / (1-(1+rate)^-number of years))

$19,467.28 = ($200,000 *Rate) / (1-(1+rate)^-30)

Rate = 0.09 or 9%

Yield to maturity is 0.09.

Alternatively in Excel using rate function:

Yield to maturity is 0.09.

Payment = Present value *Rate) / (1-(1+rate)^-number of years))