1. Consider a student loan of ​$17,500 at a fixed APR of 12​% for 20 years. What is the monthly payment?

2. Consider a student loan of ​$25,000 at a fixed APR of 6​% for 15 years. What is the monthly payment?

3. Consider a home mortgage of ​$225,000 at a fixed APR of 4.5​% for 20 years. What is the monthly payment?

4. Consider a home mortgage of ​$225,000 at a fixed APR of 6​% for 30 years. What is the monthly payment?

5. Suppose that on January 1 you have a balance of ​$3000 on a credit card whose APR is 21​%, which you want to pay off in 1 year. Assume that you make no additional charges to the card after January 1. Calculate monthly payment

6. Suppose that on January 1 you have a balance of ​$4500 on a credit card whose APR is 17​%, which you want to pay off in 3 years. Assume that you make no additional charges to the card after January 1. Calculate monthly payment

Respuesta :

a) p = Pr/[1-(1+i)^-n] 
Assuming the interest compounds monthly 
p = 175000(.01)/[1 - 1/(1.01)^240] = $1926.90 

b) 240*1926.90 = $462,456 

c) 175000/462456 = 37.84% is paid to principal and 100-37.84 = 62.16% is paid to interest.

Answer:

The EMI formula is :

[tex]EMI=\frac{p\times r\times(1+r)^{n}}{(1+r)^{n}-1}[/tex]

Part 1.

p = 17500

r = [tex]12/12/100=0.01[/tex]

n = [tex]12\times20=240[/tex]

Putting values in formula we get

[tex]\frac{17500\times0.01\times(1+0.01)^{240}}{(1+0.01)^{240}-1}[/tex]

=> [tex]\frac{17500\times0.01\times(1.01)^{240}}{(1.01)^{240}-1}[/tex]

= $192.69

Part 2.

p = 25000

r = [tex]6/12/100=0.005[/tex]

n = [tex]12\times15=180[/tex]

Putting values in formula we get

[tex]\frac{25000\times0.005\times(1+0.005)^{180}}{(1+0.005)^{180}-1}[/tex]

=> [tex]\frac{25000\times0.005\times(1.005)^{180}}{(1.005)^{180}-1}[/tex]

= $210.96

Part 3.

p = 225000

r = [tex]4.5/12/100=0.00375[/tex]

n = [tex]12\times20=240[/tex]

Putting values in formula we get

[tex]\frac{225000\times0.00375\times(1+0.00375)^{240}}{(1+0.00375)^{240}-1}[/tex]

=> [tex]\frac{225000\times0.00375\times(1.00375)^{240}}{(1.00375)^{240}-1}[/tex]

= $1423.46

Part 4.

p = 225000

r = [tex]6/12/100=0.005[/tex]

n = [tex]12\times30=360[/tex]

Putting values in formula we get

[tex]\frac{225000\times0.005\times(1+0.005)^{360}}{(1+0.005)^{360}-1}[/tex]

=> [tex]\frac{225000\times0.005\times(1.005)^{360}}{(1.005)^{360}-1}[/tex]

= $1348.98

Part 5.

p = 3000

r = [tex]21/12/100=0.0175[/tex]

n = 12

Putting values in formula we get

[tex]\frac{3000\times0.0175\times(1+0.0175)^{12}}{(1+0.0175)^{12}-1}[/tex]

=> [tex]\frac{3000\times0.0175\times(1.0175)^{12}}{(1.0175)^{12}-1}[/tex]

= $279.35

Part 6.

p = 4500

r = [tex]17/12/100=0.014166[/tex]

n = [tex]12\times3=36[/tex]

Putting values in formula we get

[tex]\frac{4500\times0.014166\times(1+0.014166)^{36}}{(1+0.014166)^{36}-1}[/tex]

=> [tex]\frac{4500\times0.014166\times(1.014166)^{36}}{(1.014166)^{36}-1}[/tex]

= $160.43