# How to solve these problems: $8,000 is to be repaid with quarterly payments #### Janahi ##### New member 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 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 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 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
What d'heck does that mean? ............. I suppose dat means review....

Have you been given financial formulas for these?
.

#### Denis

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 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 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
Amen, Father Jeff!!