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  1. MHB Apprentice

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    #1
    Hello every. I have attempted to solve six following simple interest problems, but I'm not sure if they are right. Please help. Thank you.


    1/Jane was due to make loan payments of \$1200 four months ago, \$1500 today, and \$700 in two months. Instead, she is to make a single payment today. If money is worth 9.8% and the agreed focal date is today, what is the size of the replacement payment?




    Future value=1200[1+9.8%(6/12)]= 1258.80

    Future value=1500[1+9.8%(1/12)]= 1512.25

    Present value= 700/1+9.8%(2/12)= 688.75041

    1258.80+1512.25+688.75041= 3 459.80 is the size of the replacement value.






    2/Judy received a payment of \$2950 and used it to pay back two equal outstanding loans from 45 days ago and 190 days ago. If interest is 12.5% on the loans, and the agreed focal date is today, what was the size of the equal amounts borrow?




    Unknown amount equal amount is x

    FV=x[1+12.5%(190/365)]= 1.065068x


    FV=x[1+12.5%(45/365)]=1.015410x

    1.065068x + 1.015410x = 2950


    X = 1417.94 is the equal size of each amount.





    3/ A loan of \$5000 is to be repaid in three equal installments due 60, 120, and 180 days after the date of the loan. If the focal date is the date of the loan and interest is 6.9% p.a., compute the amount of the installments.




    The amount of the installments = x

    1x/ 1+6.9%(60/365) = 0.988784743x

    1x/ 1+6.9%(120/365) = 0.97781826x

    1x/ 1+6.9%(180/365) =0.967092364x



    0.988784743x + 0.97781826x + 0.967092364x = 5000

    X= 1704.34 is the amount of each installments .




    4/ On April 1, \$25000, 364-day T-bills were auctioned off to yield 2.92%


    a/ What is the price of each \$25000 T-bill on April?
    Purchased on April 01. 364 T-bill. April 01(assuming 2016) to Mar 31 2017 = 364 days.


    Present value = 25000/1+ 2.92%(364/365) = 24292.5995 is the purchased price of \$25000 T-bill



    b/ What is the yield rate on August 15 if the market price is \$24377.64?


    April 01 to Aug 15 = 136 days



    Yield rate is unknown = r



    24377.64 = 24292.5995 [1+r(136/365)]= 0.009395139 or 0.9395%



    1.Problem number 12 on page 301 of the text.


    2.Problem number 14 on page 301 of the text.








    c/ Calculate the market value of each \$25000 T-bill on Oct 1 if the rate of return on that date is 4.545%.


    Since maturity value of T-bill is Mar 31 2017, Oct 01 2016 to Mar 31 2017 = 181days



    Present value = 25000/1+4.545%(181/365) = 24 448.96389 was the price T-bill sold.








    d/ What is the rate of return realized if a \$25000 T-bill purchase on April 1 is sold on Nov 20 at a market rate of 4.625%?


    From Nov 20 to maturity date (Mar 21 2017)= 131 days.


    Present value = 25000/1+4.625%(131/365) = 24 591.79308 was amount purchased T-bill on Nov 20.



    Now find the yield rate return of 25000 T-bill purchased on April 01 is sold on Nov 20 at rate of 4.625%.



    April 01 to Nov 20 = 233 days.

    25 591.79308 = 24 292.6 [1+r(233/365)] = 0.019293687 or 1.9393%



    5/ An investment dealer paid \$24 756.25 to acquire a \$25 000, 182-day Government of Canada treasury bill at the weekly auction. What was the annual rate of return on this bill?



    Annual rate = x

    25 000 = 24 756.25[1+r(182/365)] = 1.9746% is the annual rate of return.





    6/ At auction on June 22, 2015, \$100 000, 91-day treasury bills were sold for \$99 600. An investor purchasing one of these T-bills held it for 40 days, then sold it to yield 1.4%.



    a/ What was the original yield of the T-bill?

    100 000=99 600[1+r(91/364)] = 1.610039%



    b/At what price did the investor sell?

    100 000/1+1.4%(51/365) = 99 804.76547 was the price sold.



    c/ What annual rate of return did the investor realize while holding his T-bill?

    99 804.76547 = 99 600[1+r(51/364)] = 1.8759%

  2. MHB Journeyman
    MHB Math Helper

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    #2
    Quote Originally Posted by isuck View Post
    Hello every. I have attempted to solve six following simple interest problems, but I'm not sure if they are right. Please help. Thank you.


    1/Jane was due to make loan payments of \$1200 four months ago, \$1500 today, and \$700 in two months. Instead, she is to make a single payment today. If money is worth 9.8% and the agreed focal date is today, what is the size of the replacement payment?




    Future value=1200[1+9.8%(6/12)]= 1258.80
    Why "6/12"? If she is "late" by 4 months shouldn't that be "4/12"?

    Quote Quote:
    Future value=1500[1+9.8%(1/12)]= 1512.25
    Why "1/12". She was, initially, supposed to make the $1500 payment today, not 1 month earlier.

    Quote Quote:
    Present value= 700/1+9.8%(2/12)= 688.75041

    1258.80+1512.25+688.75041= 3 459.80 is the size of the replacement value.






    2/Judy received a payment of \$2950 and used it to pay back two equal outstanding loans from 45 days ago and 190 days ago. If interest is 12.5% on the loans, and the agreed focal date is today, what was the size of the equal amounts borrow?




    Unknown amount equal amount is x

    FV=x[1+12.5%(190/365)]= 1.065068x


    FV=x[1+12.5%(45/365)]=1.015410x

    1.065068x + 1.015410x = 2950


    X = 1417.94 is the equal size of each amount.
    That looks correct to me.




    Quote Quote:
    3/ A loan of \$5000 is to be repaid in three equal installments due 60, 120, and 180 days after the date of the loan. If the focal date is the date of the loan and interest is 6.9% p.a., compute the amount of the installments.



    The amount of the installments = x

    1x/ 1+6.9%(60/365) = 0.988784743x

    1x/ 1+6.9%(120/365) = 0.97781826x

    1x/ 1+6.9%(180/365) =0.967092364x



    0.988784743x + 0.97781826x + 0.967092364x = 5000

    X= 1704.34 is the amount of each installments .




    4/ On April 1, \$25000, 364-day T-bills were auctioned off to yield 2.92%


    a/ What is the price of each \$25000 T-bill on April?
    Purchased on April 01. 364 T-bill. April 01(assuming 2016) to Mar 31 2017 = 364 days.


    Present value = 25000/1+ 2.92%(364/365) = 24292.5995 is the purchased price of \$25000 T-bill



    b/ What is the yield rate on August 15 if the market price is \$24377.64?


    April 01 to Aug 15 = 136 days



    Yield rate is unknown = r



    24377.64 = 24292.5995 [1+r(136/365)]= 0.009395139 or 0.9395%



    1.Problem number 12 on page 301 of the text.


    2.Problem number 14 on page 301 of the text.








    c/ Calculate the market value of each \$25000 T-bill on Oct 1 if the rate of return on that date is 4.545%.


    Since maturity value of T-bill is Mar 31 2017, Oct 01 2016 to Mar 31 2017 = 181days



    Present value = 25000/1+4.545%(181/365) = 24 448.96389 was the price T-bill sold.








    d/ What is the rate of return realized if a \$25000 T-bill purchase on April 1 is sold on Nov 20 at a market rate of 4.625%?


    From Nov 20 to maturity date (Mar 21 2017)= 131 days.


    Present value = 25000/1+4.625%(131/365) = 24 591.79308 was amount purchased T-bill on Nov 20.



    Now find the yield rate return of 25000 T-bill purchased on April 01 is sold on Nov 20 at rate of 4.625%.



    April 01 to Nov 20 = 233 days.

    25 591.79308 = 24 292.6 [1+r(233/365)] = 0.019293687 or 1.9393%



    5/ An investment dealer paid \$24 756.25 to acquire a \$25 000, 182-day Government of Canada treasury bill at the weekly auction. What was the annual rate of return on this bill?



    Annual rate = x

    25 000 = 24 756.25[1+r(182/365)] = 1.9746% is the annual rate of return.





    6/ At auction on June 22, 2015, \$100 000, 91-day treasury bills were sold for \$99 600. An investor purchasing one of these T-bills held it for 40 days, then sold it to yield 1.4%.



    a/ What was the original yield of the T-bill?

    100 000=99 600[1+r(91/364)] = 1.610039%



    b/At what price did the investor sell?

    100 000/1+1.4%(51/365) = 99 804.76547 was the price sold.



    c/ What annual rate of return did the investor realize while holding his T-bill?

    99 804.76547 = 99 600[1+r(51/364)] = 1.8759%[/QUOTE]

  3. MHB Apprentice

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    Thank you HallsofIvy. I got the answers from my professor and all of my work were correct except the only wrong answer was the part b of question #4. Below are all the correct answers:

    (1)
    Future value=1200[1+9.8%(6/12)]= 1258.80
    Future value=1500[1+9.8%(1/12)]= 1512.25
    Present value= 700/1+9.8%(2/12)= 688.75041
    1258.80+1512.25+688.75041= 3 459.80

    (2)
    Unknown amount equal amount is x
    FV=x[1+12.5%(190/365)]= 1.065068x

    FV=x[1+12.5%(45/365)]=1.015410x
    1.065068x + 1.015410x = 2950

    X = 1417.94 is the equal size of each amount.

    (3)
    The amount of the installments = x
    1x/ 1+6.9%(60/365) = 0.988784743x
    1x/ 1+6.9%(120/365) = 0.97781826x
    1x/ 1+6.9%(180/365) =0.967092364x

    0.988784743x + 0.97781826x + 0.967092364x = 5000
    X= 1704.34 is the amount of each installments .

    (4)
    a/ What is the price of each $25000 T-bill on April?
    Purchased on April 01. 364 T-bill. April 01(assuming 2016) to Mar 31 2017 = 364 days.

    Present value = 25000/1+ 2.92%(364/365) = 24292.5995 is the purchased price of $25000 T-bill

    b/ What is the yield rate on August 15 if the market price is $24377.64?

    April 01 to Aug 15 = 136 days

    Yield rate is unknown = r

    622.36/24377.64(228/365) =4.09%

    c/ Calculate the market value of each $25000 T-bill on Oct 1 if the rate of return on that date is 4.545%.

    Since maturity value of T-bill is Mar 31 2017, Oct 01 2016 to Mar 31 2017 = 181days

    Present value = 25000/1+4.545%(181/365) = 24 448.96 was the price T-bill sold.




    d/ What is the rate of return realized if a $25000 T-bill purchase on April 1 is sold on Nov 20 at a market rate of 4.625%?

    From Nov 20 to maturity date (Mar 21 2017)= 131 days.

    Present value = 25000/1+4.625%(131/365) = 24 591.79308 was amount purchased T-bill on Nov 20.

    Now find the yield rate return of 25000 T-bill purchased on April 01 is sold on Nov 20 at rate of 4.625%.

    April 01 to Nov 20 = 233 days.
    25 591.79308 = 24 292.6 [1+r(233/365)] = 0.019293687 or 1.9393%

    (5)
    Annual rate = x
    25 000 = 24 756.25[1+r(182/365)] = 1.9746% is the annual rate of return.

    (6)
    a/ What was the original yield of the T-bill?
    100 000=99 600[1+r(91/364)] = 1.610039%

    b/At what price did the investor sell?
    100 000/1+1.4%(51/365) = 99 804.76547 was the price sold.

    c/ What annual rate of return did the investor realize while holding his T-bill?
    99 804.76547 = 99 600[1+r(51/364)] = 1.8759%










    The amount of the installments = x

    1x/ 1+6.9%(60/365) = 0.988784743x

    1x/ 1+6.9%(120/365) = 0.97781826x

    1x/ 1+6.9%(180/365) =0.967092364x



    0.988784743x + 0.97781826x + 0.967092364x = 5000

    X= 1704.34 is the amount of each installments .




    4/ On April 1, \$25000, 364-day T-bills were auctioned off to yield 2.92%


    a/ What is the price of each \$25000 T-bill on April?
    Purchased on April 01. 364 T-bill. April 01(assuming 2016) to Mar 31 2017 = 364 days.


    Present value = 25000/1+ 2.92%(364/365) = 24292.5995 is the purchased price of \$25000 T-bill



    b/ What is the yield rate on August 15 if the market price is \$24377.64?


    April 01 to Aug 15 = 136 days



    Yield rate is unknown = r



    24377.64 = 24292.5995 [1+r(136/365)]= 0.009395139 or 0.9395%



    1.Problem number 12 on page 301 of the text.


    2.Problem number 14 on page 301 of the text.








    c/ Calculate the market value of each \$25000 T-bill on Oct 1 if the rate of return on that date is 4.545%.


    Since maturity value of T-bill is Mar 31 2017, Oct 01 2016 to Mar 31 2017 = 181days



    Present value = 25000/1+4.545%(181/365) = 24 448.96389 was the price T-bill sold.








    d/ What is the rate of return realized if a \$25000 T-bill purchase on April 1 is sold on Nov 20 at a market rate of 4.625%?


    From Nov 20 to maturity date (Mar 21 2017)= 131 days.


    Present value = 25000/1+4.625%(131/365) = 24 591.79308 was amount purchased T-bill on Nov 20.



    Now find the yield rate return of 25000 T-bill purchased on April 01 is sold on Nov 20 at rate of 4.625%.



    April 01 to Nov 20 = 233 days.

    25 591.79308 = 24 292.6 [1+r(233/365)] = 0.019293687 or 1.9393%



    5/ An investment dealer paid \$24 756.25 to acquire a \$25 000, 182-day Government of Canada treasury bill at the weekly auction. What was the annual rate of return on this bill?



    Annual rate = x

    25 000 = 24 756.25[1+r(182/365)] = 1.9746% is the annual rate of return.





    6/ At auction on June 22, 2015, \$100 000, 91-day treasury bills were sold for \$99 600. An investor purchasing one of these T-bills held it for 40 days, then sold it to yield 1.4%.



    a/ What was the original yield of the T-bill?

    100 000=99 600[1+r(91/364)] = 1.610039%



    b/At what price did the investor sell?

    100 000/1+1.4%(51/365) = 99 804.76547 was the price sold.



    c/ What annual rate of return did the investor realize while holding his T-bill?

    99 804.76547 = 99 600[1+r(51/364)] = 1.8759%[/QUOTE][/QUOTE]

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