Question 1194151: MAT: Topics in Contemporary Math
Loans
3) Adventuresome Alex REALLY wants to buy an RV and live out in the wilderness, away
from the hassles of city living. They decide they can afford a monthly payment of $415
and their lending agency offers a 3.0% annual interest rate on a 10-year loan.
a. What is the total value of the loan?
b. What was the total amount Adventuresome Alex paid their lending agency?
c. How much did they pay in interest?
Answer by math_tutor2020(3816)   (Show Source):
You can put this solution on YOUR website!
The monthly payment formula is
P = (L*i)/( 1-(1+i)^(-n) )
where,
P = monthly payment
L = loan amount
i = interest rate per month, in decimal form
n = number of months
In this case we have,
P = 415
L = unknown and what we want to solve for
i = 0.03/12 = 0.0025 exactly
n = 12*10 = 120 months (equivalent to 10 years)
Let's plug those known values in, and solve for L
P = (L*i)/( 1-(1+i)^(-n) )
415 = (L*0.0025)/( 1-(1+0.0025)^(-120) )
415 = L * [ (0.0025)/( 1-(1+0.0025)^(-120) ) ]
415 = L * 0.00965607446983
L = 415/0.00965607446983
L = 42,978.1275296343
L = 42,978.13
which is the total value of the loan if Alex paid the max monthly payment of $415
That wraps up part (a)
For part (b), we multiply the $415 monthly payment by the 120 months to figure out how much Alex pays back (principal + interest)
415*120 = 49,800 dollars is the answer to part (b)
In part (c), we subtract the results of part (b) and part (a) in that order
49,800 - 42,978.13 = 6,821.87
That's the amount of total interest paid
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Answers:
(a) $42,978.13
(b) $49,800
(c) $6,821.87
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