Loan 30100 112 Suppose now that you struggle to find a job

Loan : $ 30,100

1.12. Suppose now that you struggle to find a job and wish to refinance at a lower monthly payment. A new bank offers to buy your loan at r = 4% annual, but pay it back over 35 years. Determine the monthly payment. 1.13. Also, determine the future value of this new loan. (Use the compounding interest formula.) This is how banks manipulate lower income individuals into paying more over the life time of a loan

Solution

(1.12)

Monthly (nominal) interest rate = 4%/12 = 0.33%

Number of months = 35 x 12 = 420

Monthly payment ($) = 30,100 / P/A(0.33%, 420) = 30,100 / 227.0773** = 132.55

**P/A(r%, N) = [1 - (1 + r)^-N] / r

P/A(0.33%, 420) = [1 - (1.0033)^-420] / 0.0033 = (1 - 0.2506) / 0.0033 = 0.7494 / 0.0033 = 227.0773

(1.13)

Future value ($) = Loan amount x F/P(r%, N) = 30,100 x F/P(0.33%, 420) = 30,100 x 3.9897** = 120,090.22

**F/P(r%, N) = (1 + r)^N

F/P(0.33%, 420) = (1.0033)⁴²⁰ = 3.9897