Question 1194151
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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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