Answer:

1. Maturity value

a. Credit union :

FV=159,264.47

b.Local bank

FV=158,254.27

c.The credit union option yields higher returns which are 159,264.47 compared to those produced by the local bank which are 158,254.27

2.

a. Value of investment at the end of year 5

FV=5,678.15

b.Total interest earned =678.15

3.Future value of the loan to be repaid

FV= 77,470.76

4.

a.Value of the loan at the end of 5 years

FV= 35,385.51

b.Value at the end of 9 years

FV= 43,621.15

5.

a.Future value

FV= 14,655.43

b.Future value

FV=15,101.19

6.

a.Principal amount

PV=21,793.03

b.

Total interest charged

=3,206.97

7.

a.Loan Balance at the end of the first year =99,546.3

b. Loan balance at the end of year 2 = 20,010.91

c.Loan balance to be repaid at the end of year 3

Fv=-21,053.57

8.Present value of amount to be invested

PV=-277,555.68

9.

You would need to invest 8.76 more 

• i.e +8.76

10. Amount borrowed

PV=43,453.19

11.Present value

PV=-27,907.25

12. Present value

PV=-2,918.19

13.Present value

PV=-2,868.26

14.Present value

• You would have to invest 7.27 less [10,773.26-10,765.99]
• i.e -7.27

15.

a.Total present value = 35,721.2154

b.Option 1 is economically better for the manufacturing firm as it would incur 6,221.2154 [35,721.2154-29,500] less by choosing option 1 instead of option 2

Step-by-step explanation

The following variables will be used throughout the calculations using a financial calculator

PV=present value

i=Discount rate/interest

Pmt=payment

FV=future value

N=Number of periods

• In the calculations to be performed you need to identify what is required to be calculated then using the remaining variables given to you,calculate that required variable
• An amount inputted with a negative sign represents an investment/outflow of cash

1.

Here what is required is the calculation of the future value which is the maturity value

a. Credit union :

N=72 [6x12]

i=0.8925  [10.71/12]

PV=-84,000

FV=159,264.47

• The interest is quoted in annual terms but because it was compounded monthly we will need to divide it by 12 to get the monthly rate i.e. 10.71/12 = 0.8925
• Because the interest is compounded monthly we will need to calculate the number of periods over which it will be compounded i.e. 6x12 =72

b.Local bank

N=12 [6x2]

i=5.42 [10.84/2]

PV=-84,000

FV=158,254.27

• The interest is quoted in annual terms but because it was compounded monthly we will need to divide it by 2 to get the Semi-annual rate i.e. 10.71/12 = 5.42%
• Because the interest is compounded semi-annually we will need to calculate the number of periods over which it will be compounded
• i.e. 6x2=12

c.The credit union option yields higher returns which are 159,264.47 which are higher than those produced by the local bank which are 158,254.27

 

2.

a. Value of investment at the end of year 5

N=10 [5x2]

i=1.28 [2.56/2]

PV=-5,000

FV=5,678.15

• The interest is quoted in annual terms but because it was compounded semi-annually we will need to divide it by 2 to get the monthly rate i.e. 2.56%/2 = 1.28%
• Because the interest is compounded semi-annually we will need to calculate the number of periods for which it will be compounded i.e. 5x2=10

b.Total interest earned 

Compound interest = Future value - principal amount

=5678.15-5,000

=678.15

 

3.What is required here is the future value of the loan to be repaid

N=3 [1.5x2]

i=2.69 [5.38/2]

PV=-66,000

FV= 77,470.76

• The interest is quoted in annual terms but because it was compounded semi-annually we will need to divide it by 2 to get the monthly rate i.e. 5.38%/2 = 2.69%
• Because the interest is compounded semi-annually we will need to calculate the number of periods for which it will be compounded i.e. 1.5x2=3 . In this case 1 year and six months are equal to 1.5 years

4.

a.Value of the loan at the end of 5 years

N=20 [5x4]

i=1 [4/4]

PV=-29,000

FV= 35,385.51

• The interest is quoted in annual terms but because it was compounded quarterly we will need to divide it by 2 to get the quarterly rate i.e. 4%/4 = 1%
• Because the interest is compounded semi-annually we will need to calculate the number of periods for which it will be compounded i.e. 5x4=20 .

b.Value at the end of 9 years

N=8 [4x2]

i=2.65 [5.30/2]

PV=-35,385.51

FV= 43,621.15

• The value of the loan at the end of the  5 years(35,385.51) which had an interest which was compounded quarterly will now be the input in calculating the loan value of the loan which is compounded semi-annually.
• The interest is quoted in annual terms but because it was compounded semi-annually you will need to divide it by 2 to get the monthly rate i.e. 5.30%%/2 = 2.65%
• Because the interest is compounded semi-annually you will need to calculate the number of periods for which it will be compounded i.e. 4x2=8

5.

a.Future value

N=1.33

i=3.5 [7/2]

PV=-14,000

FV= 14,655.43

 

• The challenge here is converting the number of months  from August 3rd,2013 to April 8th 2014(8 months) to do this you will need to convert the months into years then multiply by 2 i.e 8/12 x2 =1.33 semi annual periods
• an alternative  to  this will be : 1 semi-annual period = 6 months therefore in 8 months there is 1 full semi-annual period then two months will be left, 2 months = 2/6 =0.33(in semi-annual periods) . Total semi-annual periods =1.33 (1+0.33)
• The interest is quoted in annual terms but because it was compounded semi-annually we will need to divide it by 2 to get the monthly rate i.e. 7%/2 = 3.5%

b.Future value

N=12

i=0.25 [3/12]

PV=-14,655.43

FV=15,101.19

• From April 8th 2014 to March 23rd ,2015 its a full 12 months therefore N=12
• The interest is quoted in annual terms but because it was compounded monthly you will need to divide it by 12 to get the monthly rate i.e. 3%/12 = 0.25%
• 14,655.43 will be the present value(Future value from previous calculation)

6.

a.Principal amount

N=44 [3x12 =8]

i=0.3125 [3.75/12]

FV=-25,000

PV=21,793.03

• Here the amount owed is $25,000 but we need to calculate the principal amount before interest was accumulated to the loan amount which will be the present value
• The interest is quoted in annual terms but because it was compounded monthly you will need to divide it by 12 to get the monthly rate i.e. 3.75%/12 = 0.3125%

b.

Total interest charged

Compound interest = Future value - principal amount

=25,000-21,793.03

=3,206.97

7.

a.Loan Balance at the end of the first year

Semi-annual rate =5.88%/2 = 2.94%

first compounding balance : (160,000x2.94%) +160,000 =4,704+160,000 =164,704

Second compounding : (164,704x2.94%) +164,704 =169,546.30

Balance at the end of year 1 :169,546.30-70,000 = 99,546.3

Alternative  :

PV= 160,000

i=2.94 [5.88/2)

N=2

FV=-169,546.30

• Then  Balance at the end of year 1 :169,546.30-70,000 = 99,546.3

b. Loan balance at the end of year 2 

Quarterly rate : 5.38%/4 =1.345%

First compounding :(1.345%x99,546.3)+99,546.3 = 100,885.20

second compounding :(1.345%x100,885.20) + 100,885.20 = 102,242.1059

third compounding : (1.345%x102,242.1059)+102,242.1059 = 103,617.2622

Fourth compounding :(1.345%x103,617.2622)+103,617.2622 =105,010.91

Total loan balance at the end of the second year : 105,010.91-85,000 = 20,010.91

Alternative : 

Pv= 99,546.3

i= 1.345 [5.38/4]

N=4

Fv=-105,010.91

• Then total loan balance at the end of the second year : 105,010.91-85,000 = 20,010.91

c.Loan balance to be repaid at the end of year 3

Pv= 20,010.91

i= 0.424 [5.09/12]

N=12

Fv=-21,053.57

8.Present value of amount to be invested

N=120 [10x12]

i=0.305 [6.66/12]

FV=400,000

PV=-277,555.68

9.

Investment at a rate of 5.20% compounded monthly

N=36 [3x12]

i=0.433 [5.2/12]

FV=10,500

PV=-8,986.40

 

Investment at a rate of 5.36% compounded Annually

N=3

i=5.36

FV=10,500

PV=-8,977.64

You would need to invest 8.76 more[8,977.64-8,986.40] 

• i.e +8.76

10. Amount borrowed

N=8[4x2]

i=2.52 [5.04/2]

FV=-53,026.19

PV=43,453.19

 

11.Present value

N=10.67 [(5x12+4)/12 x2}

i=2.055 [4.11/2]

FV=34,672

PV=-27,907.25

• The same method as explained in 5.a is used to calculate N

12. Present value

N=54.4944 [4.5412x12}

i=0.33 [4.01/12]

FV=-3,500

PV=-2,918.19

13.Present value

N=4.33 [(13/12)x4]

i=1.0425 [4.17/4]

FV=3,000

PV=-2,868.26

• To calculate N you convert the months(13) from June 17,2017 to February 18,2018 years then to semi annul periods i.e 13/12 x2

14.Present value

Present value at a rate of 5.5% compounded semi-annually

N=4 [2x2]

i=2.75 [5.5/2]

FV=12,000

PV=-10,765.99

Present value at a rate of 5.54% compounded annually

N=2

i=5.54

FV=12,000

PV=-10,773.26

• You would have to invest 7.27 less [10,773.26-10,765.99]
• i.e -7.27

15.

a.Present value of option 2

N= 1   [3/12 x4]

i=1.53 [ 6.12/4]

FV=18,500

PV=-18,221.2154

• To calculate N you convert the months(3) from June 17,2017 to February 18,2018 years then to quarterly periods i.e 3/12 x4

Total present value : 18,221.2154+17,500 = 35,721.2154

• Option 1 is economically better for the manufacturing firm as it would incur 6,221.2154 [35,721.2154-29,500] less by choosing option 1 instead of option 2