with Simple Interest Problems

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In summary, Judy received a payment of $2950 and used it to pay back two loans from 45 days and 190 days ago. If interest is 12.5%, the size of the replacement payment is $3459.80.
  • #1
isuck
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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)]= 1.065068xFV=x[1+12.5%(45/365)]=1.015410x

1.065068x + 1.015410x = 2950X = 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%
 
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  • #2
isuck said:
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"?

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.

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

1.065068x + 1.015410x = 2950X = 1417.94 is the equal size of each amount.
That looks correct to me.

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
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]
 

Related to with Simple Interest Problems

1. What is simple interest and how is it different from compound interest?

Simple interest is a method of calculating interest on a loan or investment based on the original principal amount. It is calculated by multiplying the principal amount by the interest rate and the number of time periods. Unlike compound interest, which adds the accumulated interest to the principal amount to calculate new interest, simple interest does not take into account any previous interest earned.

2. How do I calculate the total amount earned with simple interest?

To calculate the total amount earned with simple interest, you can use the formula: A = P(1 + rt), where A is the total amount, P is the principal amount, r is the interest rate, and t is the number of time periods. Simply substitute the values and solve for A to find the total amount earned.

3. What factors can affect the interest rate for simple interest?

The interest rate for simple interest can be affected by a variety of factors, such as the current economic conditions, the risk level of the investment or loan, and the amount of competition in the market. Additionally, the interest rate may be influenced by the creditworthiness of the borrower or the credit rating of the institution offering the investment or loan.

4. Can simple interest be used for both loans and investments?

Yes, simple interest can be used for both loans and investments. For loans, it is used to calculate the interest payable by the borrower to the lender. For investments, it is used to calculate the interest earned by the investor from the institution offering the investment.

5. Is simple interest the most accurate method for calculating interest?

No, simple interest is not the most accurate method for calculating interest. It does not take into account the compounding effect of accumulated interest, which can result in a lower overall return on an investment or a higher cost for a loan. Compound interest, on the other hand, takes into account the accumulated interest and is considered to be a more accurate method of calculating interest.

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