3. On 1/01/2013, an investor purchases a $100,000 bond that pays $4,000 of inter
ID: 2378946 • Letter: 3
Question
3. On 1/01/2013, an investor purchases a $100,000 bond that pays $4,000 of interest annually on 12/31 and matures on 12/31/2017. What amount should the investor be willing to pay for the bond assuming she demands a 6% annual rate of return?
4. On January 1, 2013, Glanville Co. sold goods with a cash selling price of $82,000 to Otter Corporation. Rather than paying cash, Otter signed a noninterest-bearing note requiring six annual payments of $15,000 with the first payment due on December 31, 2013. What is the implicit annual interest rate being charged by Glanville?
5. Mary Alice just won the lottery, and is trying to decide between either receiving 25 annual cash payments of $250,000 with the first payment today, or receiving a cash payment today. Mary Alice demands an annual return of 4%. At what cash payment amount would she be indifferent between the two alternatives?
Explanation / Answer
3)
Maturity period = 5 years.
Total interest paid = $4000*5 = $20000
Let P = payment to be made for the bond.
Rate of return = 6%
So, P(1+0.06)^5 = P+20000
1.338P-P = 20000
P = 20000/0.338 = 59132 $
The investor shoul pay 59132 $ for the bond
4)
Total payment made = $15000*6 = $90000
Time = 6 years.
Let rate of interest be r% per annum
Now, 90000 = 82000(1+0.01r)^6
(1+0.01r)^6 = 90000/82000 = 1.0975
1+0.01r = 1.0156
r = (1.0156-1)/0.01 = 1.56
Implicit annual interest rate charged by Glanville = 1.56%
5)Total Money received by annual cash payments = 250000*25 =$ 6250000
Let the single overall cash payment = P.
First payment is today. So the 25th payment will be after 24 years.
So, P[1+0.04]^24 = 6250000
Thus, 2.5633P = 6250000
P = 6250000/2.5633 = 2438259 $
A cash payment amount of $ 2438259 today, she will be indifferent to the two alternatives.
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