1. ## Please I Need Help with Simple Interest Problems

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. ## Re: Please I Need Help with Simple Interest Problems Hey my fellow Canuck, you posted 6 problems and showed no work. We help...we do NOT do your homework. It will be to your advantage to post over again: ONLY one problem per thread; show where you're stuck. 3. ## Re: Please I Need Help with Simple Interest Problems Hey fellow DenisB. I'm not sure what you meant by showing my work, but I tried my best by finding the numbers of days between two dates. I also showed my future and present value for each required question, and the return rate. For each question I also showed the answer, so not sure what else I needed to do. I agree, next time I probably post each problem in separate thread. Originally Posted by DenisB Hey my fellow Canuck, you posted 6 problems and showed no work. We help...we do NOT do your homework. It will be to your advantage to post over again: ONLY one problem per thread; show where you're stuck. 4. ## Re: Please I Need Help with Simple Interest Problems Originally Posted by isuck 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.
1200 * (1 + .098/12)^4 = 1239.68
1500
700 / (1 + .098/12)^2 = 688.71

1239.68 + 1500.00 + 688.71 = 3428.39

Well, at least we agree on the 688.71 !

Why 6 months on the 1200? Should be 4.
Why change the 1500: due and paid today ?

Start showing your calculations accurately: .098, NOT 9.8%

5. ## Re: Please I Need Help with Simple Interest Problems

My mistake. There were two similar questions with different values so it made me confused. The below is the correct one, but I think it's right. The only thing is my formula is different than yours probably because of different textbook.

1/Jane was due to make loan payments of $1200 six months ago,$1500 one month ago, 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. 6. ## Re: Please I Need Help with Simple Interest Problems Did you read my reply? I'm telling you that 3459.80 is NOT correct. 7. ## Re: Please I Need Help with Simple Interest Problems Beer soaked ramblings follow. Originally Posted by DenisB Did you read my reply? I'm telling you that 3459.80 is NOT correct. Nay Sir D, I say nay. I say isuck's answer of 3,459.80 be correct if his/her corrected information is correct. 8. ## Re: Please I Need Help with Simple Interest Problems Originally Posted by isuck My mistake. There were two similar questions with different values so it made me confused. The below is the correct one, but I think it's right. The only thing is my formula is different than yours probably because of different textbook. Jane was due to make loan payments of 1200 six months ago,1500 one month ago, 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. Present value= 700/1+9.8%(2/12)= 688.75041 should be Present value= 700/[1+9.8%(2/12)]= 688.75041 9. ## Re: Please I Need Help with Simple Interest Problems Beer soaked ramblings follow. Originally Posted by isuck 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
Should be x/[1+6.9%(60/365)]
1x/ 1+6.9%(120/365) = 0.97781826x
Should be x/[1+6.9%(120/365)]
1x/ 1+6.9%(180/365) =0.967092364x
Should be x/[1+6.9%(180/365)]

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

10. ## Re: Please I Need Help with Simple Interest Problems

Originally Posted by isuck
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. Agree. Personally, I prefer to write an equation of value like 2950=x(1+.1250*190/365)+x(1+.1250*45/365) 11. ## Re: Please I Need Help with Simple Interest Problems Originally Posted by isuck 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%
Answers from problems 4 to 6 all seem to be correct.
My only objections are the incorrect use of the equal sign whenever r is being computed (double arrows strongly recommended plus the proper placement of the variable r to avoid penalties) and the absence of brackets in several places like those that I pointed out earlier in post no. 8 & 9

Note: Too sober at the moment to point out exactly my objections.

12. ## Re: Please I Need Help with Simple Interest Problems

Originally Posted by jonah
Nay Sir D, I say nay.
I say isuck's answer of 3,459.80 be correct if his/her corrected information is correct.
Well, I'm from now on staying away from silly focal dates...
Glad to see yer temporarily sober Sir Jonah; an occasion to celebrate!!

14. ## Re: Please I Need Help with Simple Interest Problems

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%