How to solve these problems: $8,000 is to be repaid with quarterly payments

Janahi

New member
Joined
Dec 9, 2018
Messages
3
Hi all

Can anyone help me with the solution of those 2 problems for my final exam revision

1) A loan of $8,000 is to be repaid with quarterly payments for two years with an interest rate of 4%
compounded quarterly. Find the quarterly payment and construct an amortization schedule

Given:
Solution:
a.
b.
c.
Amortization Schedule

2) ADG Company issues $1,000,000 worth of bonds to raise capital to improve its company’s facilities.
What semi-annual deposits must be made into a sinking fund earning interest at 8% compounded semi-
annually to redeem the bonds at the end of 15 years? Construct a sinking fund schedule for the first 2
years.

Given:
Solution:
a.
b.
c.
Sinking Fund Schedule
 

Subhotosh Khan

Super Moderator
Staff member
Joined
Jun 18, 2007
Messages
18,138
Hi all

Can anyone help me with the solution of those 2 problems for my final exam revision

1) A loan of $8,000 is to be repaid with quarterly payments for two years with an interest rate of 4%
compounded quarterly. Find the quarterly payment and construct an amortization schedule

Given:
Solution:
a.
b.
c.
Amortization Schedule

2) ADG Company issues $1,000,000 worth of bonds to raise capital to improve its company’s facilities.
What semi-annual deposits must be made into a sinking fund earning interest at 8% compounded semi-
annually to redeem the bonds at the end of 15 years? Construct a sinking fund schedule for the first 2
years.

Given:
Solution:
a.
b.
c.
Sinking Fund Schedule
Please share with us, your work/thoughts re. this assignment.
 

Denis

Senior Member
Joined
Feb 17, 2004
Messages
1,467
Can anyone help me with the solution of those 2 problems for my final exam revision
What d'heck does that mean?

Have you been given financial formulas for these?
 

Janahi

New member
Joined
Dec 9, 2018
Messages
3
Please share with us, your work/thoughts re. this assignment.
Here is my trying work
Given
Pv= $8000 M=4 t=2 years
j= 4%/100= 0.04
Ra= ?
Solution:
a. I= j/m= 0.04/4= 0.01
b. n= t*m= 2*4=8
c. Ra= Pv * I/ 1(1+i)-n
8000*0.01/1-(1+0.01)-8= 1045.52


Given:
Pv=1,000000 m=2 (not sure if this no. for semi annually)
j= 8%/100= 0.08
t= 15 years

Solution:
a. I= 0.08/2= 0.4
b. n= t*m= 5*2= 30
c. Ra= PV*I/1-(1+i)-n
1,000000*0.04 / 1-(1+0.04)-30 = 5783.09
 

Subhotosh Khan

Super Moderator
Staff member
Joined
Jun 18, 2007
Messages
18,138
What d'heck does that mean? ............. I suppose dat means review....

Have you been given financial formulas for these?
.
 

Denis

Senior Member
Joined
Feb 17, 2004
Messages
1,467
Pv= $8000 M=4 t=2 years
j= 4%/100= 0.04
Ra= ?
Solution:
a. I= j/m= 0.04/4= 0.01
b. n= t*m= 2*4=8
c. Ra= Pv * I/ 1(1+i)-n
8000*0.01/1-(1+0.01)-8= 1045.52
Not sure what that means or comes from...but it's CORRECT!!
Standard formula for loan payment calculation is:
p = a*i / [1 - 1/(1 + i)^n]
where:
a = amount of loan (8000)
i = interest factor (.04/4 = .01)
n = number of payments (8)
p = payment (?)

p = 8000*.01 / [1 - 1/(1+.01)^8] = 1045.522336.....
 

Denis

Senior Member
Joined
Feb 17, 2004
Messages
1,467
Pv=1,000000 m=2 (not sure if this no. for semi annually)
j= 8%/100= 0.08
t= 15 years
Solution:
a. I= 0.08/2= 0.4
b. n= t*m= 5*2= 30
c. Ra= PV*I/1-(1+i)-n
1,000000*0.04 / 1-(1+0.04)-30 = 5783.09
Again, strange stuff for me; but 5783.09 is way too low...
Standard formula:
p = f*i / [(1 + i)^n - 1]
where:
f = future value (1000000)
i = interest factor (.08/2 = .04)
n = number of periods (15*2 = 30)
p = payment required (?)

p = 1000000*.04 / [(1 + .04)^30 - 1] = 17830.10
 

JeffM

Elite Member
Joined
Sep 14, 2012
Messages
3,236
Here is my trying work
Given
Pv= $8000 M=4 t=2 years
j= 4%/100= 0.04
Ra= ?
Solution:
a. I= j/m= 0.04/4= 0.01
b. n= t*m= 2*4=8
c. Ra= Pv * I/ 1(1+i)-n
8000*0.01/1-(1+0.01)-8= 1045.52


Given:
Pv=1,000000 m=2 (not sure if this no. for semi annually)
j= 8%/100= 0.08
t= 15 years

Solution:
a. I= 0.08/2= 0.4
b. n= t*m= 5*2= 30
c. Ra= PV*I/1-(1+i)-n
1,000000*0.04 / 1-(1+0.04)-30 = 5783.09
Denis,

His notation is a bit strange, but not indecipherable.

\(\displaystyle p = \dfrac{ai}{1 - \left ( \dfrac{1}{1 + i} \right )^n}\)

In step a, he calculates the periodic interest rate from the annual rate, or i.

In step b, he calculates the number of periods, or n.

In step c, he apparently uses the correct formula but writes it down incorrectly in two different ways. Pieces are missing, and he uses a minus sign for exponentiation.

For the second problem, it gets weirder. In step b, he multiplies 5 times 2 and get 30, but he meant to write down 15 * 2, which does equal 30. Just a typo, I think. The correct formula is

\(\displaystyle \dfrac{fi}{(1 + i)^n - 1}.\)

Here, he again writes down the formula incorrectly and again uses a minus sign for exponentiation. This time he does not use the correct formula.

He really needs to memorize the correct formulas. Otherwise, he may not get full credit even when he gets the correct numeric answer and may easily miss the correct numeric answer by using some goofy formula.
 
Last edited:

Denis

Senior Member
Joined
Feb 17, 2004
Messages
1,467
Amen, Father Jeff!!
 
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