Question 1199180: Consider a student loan of $22,500 at a fixed APR of 12% for 25 years
A.Calculate the monthly payment
B.Determine the total amount paid over the term of the loan
C. Of the total amount paid what percentage is paid towards the principal and what is percentage is paid interest
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
Part (A)
Monthly payment formula
P = (L*i)/( 1 - (1+i)^(-n) )
where,
L = loan amount
i = monthly interest rate in decimal form
n = number of months
In this problem:
L = 22500
i = 0.12/12 = 0.01
n = 25*12 = 300 months (equivalent to 25 years)
Let's find the monthly payment
P = (L*i)/( 1 - (1+i)^(-n) )
P = (22500*0.01)/( 1 - (1+0.01)^(-300) )
P = 236.975431994467
P = 236.98
The monthly payment is $236.98
Verifying this result:
You can use a TVM solver such as this one
https://www.geogebra.org/m/mvv2nus2
which emulates the TVM solver in a TI83 and TI84.
The inputs will be:
N = 300
I% = 12
PV = 22500
PMT = left blank or set to whatever you want
FV = 0
P/Y = 12
C/Y = 12
Do not type dollar signs or commas into any of the boxes.
Here's an explanation of each input:- N = number of months in this case
- I% = annual interest rate in percent form (not decimal form)
- PV = present value, aka starting balance, aka loan amount
- FV = 0 since we want the future value of the loan, aka final balance, to be $0 when it's all paid off
- P/Y = 12 means there are 12 payments per year
- C/Y = 12 means there are 12 compounding periods per year
After the items are filled into the proper boxes, press the "Solve for PMT" button to have -236.98 show up in that box.
This value is negative to represent a cash outflow.
Here is another free online calculator you can use to verify the monthly payment:
https://www.calculator.net/loan-calculator.html
There are many other options as well.
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Part (B)
The monthly payment is $236.98 found in part (A).
It is done for 300 months (aka 25 years)
This assumes no refinancing is done.
300*236.98 = 71,094
Therefore, a total of $71,094 is paid back.
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Part (C)
The previous part found that $71,094 was paid back in total.
This consists of principal, aka the amount loaned, and interest.
Divide the loan amount over this total paid back
22500/71094 = 0.31648 = 31.648% approximately
This is the percentage of the total paid toward principal.
The remaining 100% - 31.648% = 68.352% is paid toward interest.
Another way to calculate it:
interest = (amount paid back) - (principal)
interest = (71094) - (22500)
interest = 48594 dollars
percent paid interest = (interest/totalPaid)*100%
percent paid interest = (48594/71094)*100%
percent paid interest = (0.68352)*100%
percent paid interest = 68.352%
and,
percent paid principal = 100% - (percent paid interest)
percent paid principal = 100% - (68.352%)
percent paid principal = 31.648%
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Answers:
(A) Monthly payment = $236.98
(B) Total amount paid = $71,094
(C) 31.648% toward principal, 68.352% to interest
The decimal values in part (C) are approximate.
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