Question

Jason is considering taking out a 20-year loan with monthly payments of $140 at an APR of 5.1%, compounded monthly, and this equates to a loan of $21,037.05. Assuming that the APR and the length of the loan remain fixed, which of these is a correct statement?

A.If Jason's monthly payment were $190, the amount of the loan that he is considering taking out would be less than $21,037.05.

B.If Jason's monthly payment were $110, the amount of the loan that he is considering taking out would be more than $21,037.05.

C.If Jason's monthly payment were $130, the amount of the loan that he is considering taking out would be less than $21,037.05.

D.If Jason's monthly payment were $120, the amount of the loan that he is considering taking out would be more than $21,037.05.

Answer 1

C - If Jason's monthly payment were $130, the amount of the loan that he is considering taking out would be less than $21,037.05.

Explanation:

The EMI formula is :

`(p*r*(1+r)^(n) )/((1+r)^(n)-1 )`

here r = 5.1/12/100=0.00425

p = 21037.05

and n = 20*12 = 240

Putting the values in formula we get

`(21037.05*0.00425*(1.00425)^(240) )/((1.00425)^(240)-1 )`

= (21037.05*0.00425*2.767)/1.767 = $140.00

Hence, for an amount of $21,037.05, the monthly payment becomes $140. So, if Jason is paying $130, he must have taken less loan than $21037.05.

So, option C is correct.

If you want to calculate, lets take p = x and emi = 130 and put the values in above formula. (r and n are same)

130=(x*0.00425*2.767)/1.767

130= 0.0066x

x = $19696.96(approx) (This shows that the loan will be less than $21037.05)