SOLUTION: MAT: Topics in Contemporary Math Loans 1) Suppose you got tired of paying rent and decided to buy a house. I know, it’s just that easy! After your initial down payment,

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Question 1194149: MAT: Topics in Contemporary Math
Loans
1) Suppose you got tired of paying rent and decided to buy a house. I know, it’s just that
easy! After your initial down payment, your monthly mortgage payment is $750 and the
terms of the mortgage are 3.6% annual interest for 30 years. What was the total amount
of the loan?
Answer by math_tutor2020(3817)   (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 = 750
L = unknown and what we want to solve for
i = 0.036/12 = 0.003 exactly
n = 12*30 = 360 months (equivalent to 30 years)

Let's plug those known values in, and solve for L
P = (L*i)/( 1-(1+i)^(-n) )
750 = (L*0.003)/( 1-(1+0.003)^(-360) )
750 = L * [ (0.003)/( 1-(1+0.003)^(-360) ) ]
750 = L * 0.00454645350226
L = 750/0.00454645350226
L = 164,963.745835558
L = 164,963.75

Answer: $164,963.75

Side notes:
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