CUNY Bernard M Baruch College Market Value of The Bond Questionnaire

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Mathematics

CUNY Bernard M Baruch College

Question Description

I'm working on a mathematics multi-part question and need an explanation and answer to help me learn.

Assume Mr. Smith has reached retirement and has $250,000 in an account which is earning 6.5%. He would now like to make equal monthly withdrawals for the next 15 years to completely deplete this account. Find the withdrawal payment.

A ten-year $1,000 bond pays $35 every six months. If the current interest rate is 8.2%, find the fair market value of the bond.

  1. Hint: You must do the following.
  2. Find the present value of $1000.

Find the present value of the $35 payments.

The fair market value of the bond = a + b

  • An amount of $200,000 is borrowed for 5 years at a rate of 12%. Make an amortization schedule showing the quarterly payment, the quarterly interest on the outstanding balance, the portion of the payment going toward reducing the debt, and the balance.
  • Jane plans to buy a house in 10 years. The house she dreams about costs about $150,000 today. The cost of houses increases at 2.5% per year. 
  • How much will the house cost in ten years?

Jane currently has $75,000 that she can invest to earn 3% interest over the next ten years. How much will Jane accumulate from her investment of 75,000 Dollars in ten Years?

  1. How much additional money would Jane need in ten years? In effect, how much money does Jane need to borrow to purchase her house?
  2. Prepare an amortization table to pay off Jane’s mortgage, if she can borrow at an annual rate of 6.5% to pay off the mortgage quarterly in 5 years after buying the house

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Explanation & Answer

View attached explanation and answer. Let me know if you have any questions.

Questions :
1. Assume Mr. Smith has reached retirement and has $250,000 in an account which is
earning 6.5%. He would now like to make equal monthly withdrawals for the next
15 years to completely deplete this account. Find the withdrawal payment.
Answer 1 :
Using the Formula PV = 𝑃𝑀𝑇[1 βˆ’

π‘Ÿ βˆ’π‘›π‘‘
𝑛
π‘Ÿ
𝑛

(1+ )

]

We need to calculate PMT, with PV = $250,000 & r = 0.065, with n = 12 months and t = 15
years. Giving the following :
250000= 𝑃𝑀𝑇[1 βˆ’

(1+

0.065 βˆ’12.15
)
12
0.065
12

]

250000

Hence : PMT = 114.802 = $2177.77 π‘ŠπΌπ‘‡π»π·π‘…π΄π‘Šπ΄πΏ π‘ƒπ΄π‘Œπ‘€πΈπ‘π‘‡.
2. A ten-year $1,000 bond pays $35 every six months. If the current interest rate is
8.2%, find the fair market value of the bond.
Answer 2 :
Number of installment = 10 years * 2 Payments every year = 20.
Calculating the PV of maturity = FV/(1+ * r)^t = 1000/(1+0.082)^20
= 1000/4.8366 = $206.75
=> Present value of bon interest : Current Interest * PV(AF)
= (35/1.082+1)+ (35/1.082+1)^2 +… + (35/1.082+1)^20 = 35*0.924*(1-0.206/1-0.924)
= $337.63
Meaning the fair value of bond = PV of Markets ...

QbpgbeZruqv (476)
Cornell University

Anonymous
Excellent resource! Really helped me get the gist of things.

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