BMAT 230 Test 1 Vretta Review F2015 PDF

Preview

Summary

TEST 1...

Description

BMAT 230 Test 1 Vretta Review Some timeline diagrams are included here but they are not complete. Arrows, present values and future values, t or n values should be added to your diagrams. Try to do these questions without looking at the solutions. There are answers, and then mostly full solutions for each question. #1 Zack wanted to propose to his girlfriend and decided to give her a diamond ring. The ring he liked was selling for $3200 but he only had $1500 with him. His friend, Ethan, agreed to loan him the remaining amount at an interest rate of 12% p.a. If Zack returned the money in 40 days, what amount of interest did he have to pay Ethan for the loan? #2 Isabella heard that if she invested her savings in a 91-day short-term investment at her local bank, she would earn interest at a simple interest rate of 3.5% p.a. What amount did she invest and what amount of interest did she earn from this investment if she received $11,950 at the end of the period? #3 A loan of $15,000 at 9% p.a. is to be settled in three installments as follows: first payment of $5000 in three months, and two equal payments, one in six months, and the other in nine months. What is the size of the equal payments? Let the focal date be three months from now. Include a well-labelled timeline diagram. #4 Texas Equipments wanted to invest in a high-return investment fund that promises to triple its investment at 14.92% compounded quarterly. How long would it take for the investment to mature? Express the answer in years and months, rounded up to the next month. #5 Tom is offered a loan from Bank A at 8% compounded semi-annually. Bank B offers similar terms, but at a rate of 8.16% compounded annually. Which loan should he accept? Show calculations to support your answer. #6 Rodica borrowed $6899 some time ago and she repaid the loan on September 21, 2015. She was charged a rate of interest of 0.58% p.m. and she had to pay interest of $152.35. Round the number of days up to the next day. On what initial date did Rodica obtain the loan? #7 Sandra invested a certain amount of money at 4% p.a. and another $6000 at 4.2% p.a. After 18 months, the total interest from both investments was $1098. What amount was invested at 4% p.a.? #8 What amount invested today would yield $50,000 in 4 years and 5 months if it were invested at 5.55% compounded semi-annually?

#9 If money earns 4% compounded semi-annually, what two equal payments, one in one year and the other in three years, would be equivalent to: a. $8000 today? b. $5650 due one year ago, but not paid, and $6800 due two years ago, but not paid? Include a well-labelled timeline diagram. #10 What is the accumulated amount, compound interest, and effective interest rate (expressed as a percentage to 1 decimal place) on a loan of $45,000 for four years? The rate of interest for the first year was 5% compounded semi-annually and for the next three years was 4.5% compounded quarterly. Include a well-labelled timeline diagram. #11 Harriet was supposed to pay $1275 that was due on July 21, 2015 and is supposed to pay $765 that is due on October 15, 2015 to clear a loan that she borrowed from Harvey. Instead, Harriet promised to pay $800 on November 15, 2015 and the balance on March 2, 2016. How much would Harriet have to pay Harvey on March 2, 2016 if the interest charged is 0.64% p.m. and the agreed focal date is on March 2, 2016? Include a well-labelled timeline diagram. #12 Marcia invested $25,000 at 4.5% compounded monthly for the first two years and at 5% compounded quarterly for the third year. What is the maturity value of her investment and the amount of interest earned at the end of three years? Include a welllabelled timeline diagram. #13 If you have $250,000 in your savings account and wish to grow it to a million dollars in 40 years, what is the nominal interest rate compounded semi-annually? Express the nominal rate as a percentage to 3 decimal places. #14 What nominal interest rate compounded semi-annually would place you in the same financial position as 6.16% compounded quarterly? Express the answer as a percentage to 2 decimal places. #15 Babiya borrowed a total of $3250 to pay for college fees. $2000 of this was from a bank at 6.25% p.a. and the remainder from a credit union at 0.9% p.m. What total interest should she have paid after 9 months for both loans? #16 Roshan invested $9180 in an account that was earning simple interest at a rate of 3.75% p.a. How many months did it take for his investment to earn $172.10? Round your answer off to the nearest month. #17 A company has the following payment options to settle a loan: a. pay $19,000 today or b. pay $10,000 today and $9500 in one year. If money earns 4% compounded quarterly, which option is more economical for the company and by how much? Include a well-labelled timeline diagram.

#18 You are expected to settle a loan by making payments of $1200 in one year, $1560 in two years, and $3200 in three years. What single payment in two years would be equivalent to these scheduled payments if money is worth 6% compounded semiannually? Include a well-labelled timeline diagram. #19 A loan of $3700 charging simple interest for 1 year and 3 months requires a repayment of $3954.38. If 1% was deducted from the interest rate, what would have been the repayment amount? #20 Randy has a car loan where he was supposed to pay $7500 in 9 months and $10,000 in 18 months. Instead, he will make two equal payments: one in 6 months and another in 1 year. What is the value of the equal payments assuming that money earns 4.2% compounded quarterly? Include a well-labelled timeline diagram. #21 Philip has two outstanding payments for a loan that he gave his friend: $3650, due two months ago, and another payment of $900, due in eight months. If his friend promises to make one single payment in five months that would be equivalent to both these payments, what should be the size of the payment? Assume that money earns 3% p.a. simple interest and use ‘today’ as the focal date. Include a welllabelled timeline diagram. #22 Zoey borrowed $2250 from her friend Tamer for her vacation to Halifax. If he charged her $120 in interest for 180 days, what is the monthly simple interest rate charged? Express your answer as a percentage to 4 decimal places.

Answers: #1

$22.36

#2

$11,846.63 and $103.37

#3

$5342.56

#4

7 years and 6 months

#5

either one; they are equivalent at 8.16%

#6

May 29, 2015

#7

$12,000

#8

$39,261.23

#9

$4326.34

#10

$54,070.78, $9070.78, 4.7%

#11

$1304.56

#12

$28,743.10, $3734.10

#13

3.496% compounded semi-annually

#14

6.21% compounded semi-annually

#15

$195.00

#16

6 months

#17

$19,000 today by $129.31

#18

$5849.39

#19

$3908.13

#20

$8595.28

#21

$4607.49

#22

0.9012% p.m.

Mostly full solutions: #1

t 40 days 

40 year 365

Amount loaned by Ethan to Zack = 3200

−¿

1500 = $1700

 40  I Prt 1700  0.12    $22.356164 $22.36  365  Zack would have to pay an interest of $22.36 to Ethan.

#2

S 11,950 P  $11,846.63 1 rt 1 0.035 91 365 I=S

–

P = 11,950 – 11,846.63 = 103.37

Isabella invested $11,846.63 and earned interest of $103.37.

#3

$15,000 today

3 mo. $5000

r = 0.09 p.a.

6 mo. x

9 mo. x

FD S1 5000  P2  P3

P1  1  rt 1  5000 

S2 S3   1 rt 2   1 rt 3 

x x 3  15,000 1  0.09   5000   12   1  0.09  3   1  0.09  6       12   12   15.337.50 5000  0.97799511 x  0.956937799 x

x = 5342.56 Therefore the amount of the two equal payments one in six months and one in nine months is $5342.56.

#4

Let PV = 1, FV = 3 0.1492 i  0.0373 4 n = ? (quarters) FV 3     ln  ln   PV    1   29.99936608quarters n  ln 1  i  ln 1.0373 1 year t  29.99936608 quarters  7.499841519 years 4 quarters 12 months t  7 years  0.499841519 years  1 year t  7 years  5.998098232 months t  7 years  6 months It will take 7 years and 6 months for the bond to mature.

#5

i

Bank A:

0.08 0.04 2

m 2

f 1  i   1 1.04   1 0.0816 8.16% 2

m

Bank B:

i

0.0816  8.16%  f 1

Since both rates are equivalent, Tom should accept either of the two loans.

#6

$6899 ?

I Prt

Sept. 21, 2015 (day 264)

I 150.35 1 year  3.757416117 mo  Pr 6899 0.0058 12 mo 365 days 0.31311801 year  year 114.2880738 days  up to 115 days

t

day 264 – 115 days = day 149 → May 29 Rodica obtained the loan on May 29, 2015.

#7

 18 I Prt  6000 0.042   $378  12  I = 1098 – 378 = $720 I 720 $12, 000 P  rt 0.04 1.5

The amount that was invested at 4% p.a. was $12,000. i

#8

0.0555 0.02775 2

n

53   2 8.83 12  8.83

$39, 261.23 PV FV 1 i  50,000 1.02775  The investment made today that would yield the given future value is $39,261.23.  n

#9

a.

$8000 today FD

1 year x

3 years x

8000 PV1  PV2

8000  FV1 1  i 

n

 FV2 1  i 

2

8000  x 1.02   x 1.02 

 n

6

8000 0.961168781x  0.887971382 x 8000 1.849140163 x x  $4326.34 The two equal payments are $4326.34 each are equivalent to $8000 today. b.

$6800

$5650

2 yrs. ago

1 yr ago

today

1 year x

3 years x FD

FV 1  FV 2 FV 3  x PV 1  1 i  1  PV 2  1 i  2  PV 3  1 i

 x 10 8 4 6800 1.02   5650 1.02  x 1.02   x n

n

n3

8289.162056  6619.875503 1.08243216x  x 14,909.03756 2.08243216x x $7159.43

#10

The two equal payments are $7159.43 each. $45,000 today

1 year

0.05 0.025 2 n1 2 1 2

i

FV  PV 1 i



n

4 years 0.045  0.01125 4 n 2 4 3 12

i

 45,000 1.025   $47, 278.125 2

at 1 year

FV 47, 278.125  1.01125 $54, 070.78 12

I  FV  PV 54,070.78  45,000 $9070.78 Effective rate of interest is annual rate compounded annually, n 1 4 4 1

1

 FV  n  54,070.78 4 i    1    1 0.046977938  4.7%  PV   45,000  The accumulated amount is $54,070.78, the compound interest is $9070.78, and the effective rate of interest is 4.7%.

#11

$1275 July 21, 2015

$765 Oct. 15, 2015

Nov. 15, 2015

Mar. 2, 2016

$800

x FD

r = 0.0064 p.m. S 1  S 2 S 3  x P1  1  rt1  P2  1  rt 2  P3  1  rt 3  x

 225   139   108  1275  1  0.0064  12   765  1 0.0064  12  800  1 0.0064  12   x 365 365 365       1335.361644 787.3740493 818.1795068  x 2122.735693 818.1795068  x x $1304.56

Harriet would have to pay Harvey $1304.56 on March 2, 2016.

#12

$25,000 today

2 years 3 years 0.05 0.045 i 0.0125 i  0.00375 12 4

n1 12 2 24

FV  PV 1 i

n2 4 1 4



n

FV1 25,000  1.00375

24

$27,349.75294

at 2 years

FV2 27,349.75294 1.0125  $28,743.10 4

The maturity value of the investment is $28,743.10. I = FV – PV = 28,743.10– 25,000 = $3734.10 The interest earned from the investment was $3734.10. i ?  semi  annual 

#13

m 2

1

n 2 40 80

1

 1,000,000  40  FV  n i   1     1 0.017479692 1.74796921%  PV   250,000  j mi 2 1.74796921% 3.495938421% 3.496% The nominal interest rate is 3.496% compounded semi-annually.

#14

0.0616  0.0154 4 m1 4

i1 

m1

i2 ? m2 2 4

i2  1  i1 m 2  1  1.0154  2  1 0.03103716 j2 m2 i2 2 3.103716% 6.207432% 6.21% A nominal rate of 6.21% compounded semi-annually would place me in the same financial position as 6.16% compounded quarterly. t 9 months 

#15

9 year 12

 9 I Prt 2000  0.0625    $93.75  12  First interest P = 3250 – 2000 = $1250 Second interest

I  Prt 1250  0.009   9  $101.25

I = 101.25 + 93.75 = $195.00

Therefore, the total interest Babiya should pay after 9 months is $195.00. I Prt #16

t

I 172.10 12 mo  0.499927378 year  5.99912854 mo  6 mo Pr 9180 0.0375 1 year

It took Roshan 6 months for his investment to earn $172.10. #17 $10,000

$9500

today FD i

1 year

0.04 0.01 4

n 4 1 4

Option b. = $10,000 + PV n 10,000  FV  1 i 10,000  9500  1.01

4

10,000  9129.313273 $19,129.31 Difference = 19,129.31 – 19,000 = $129.31 The option of paying $19,000 today is the more economical option by $129.31. #18 $1200

$1560

$3200

today

1 year

2 years

x i

0.06 0.03 2

FD FV1  1560  PV 2  x

PV 1  1 i   1560 FV 2  1 i  x n

1200  1.03  1560  3200  1.03 2

n

 2

x

1273.08 1560  3016.306909 x x $5849.39

3 years

A single payment of $5849.39 is equivalent to these scheduled payments. #19

15 t = 1 year and 3 months = 15 months = 12 = 1.25 years

−¿ P = 3954.38 −¿

I=S r

3700 = $254.38

254.38 I   0.055001081 Pt 3700 1.25

New interest rate = 0.055001081 −¿

0.01 = 0.045001081 p.a.

S P 1  rt  3700 1 0.045001081 1.25  $3908.13

The repayment amount would have been $3908.13. #20 $7500 6 mo.

9 mo.

$10,000 1 year

x

18 mo.

x i

FD PV 1  PV 2  x  PV 3 FV 1 1i



  x  FV 3 1i  1 4 2 7500 1.0105  10,000 1.0105  x  x 1.0105  n

 FV 2 1i

n

n

7422.068283  9590.797659  x  0.97932618 x 17,012.86594 1.97932618x x $8595.28 The value of each equal payment is $8595.28.

0.042 0.0105 4

#21 $3650

$900

2 mo. ago

today FD

5 mo. x

8 mo.

r = 0.03 p.a. S 1  P2 P3 P1  1 rt 1 

S2 S  3 1  rt 2 1  rt 3

x 2 900 3650 1  0.03     12  1  0.03  8 1  0.03  5  12 12 3668.25 882.3529412 0.987654321x 4550.602941 0.987654321x

x = $4607.49 The single payment in 5 months that is equivalent to the two original payments is $4607.49 when the focal date is today. t

#22

P = $2250,

180 12 365 , I = $120, r = ?

I Prt

r

I 120  0.009012346 0.9012% Pt 2250 180 365 12

Therefore, the rate of interest charged was 0.9012% p.m....