Question

Alex Dunphy borrows $26,000 to pay for her Caltech’s tuition. The adjustable rate loan carries a 6% annual percentage rate for the first 5 years. After that the rate will be adjusted downward to 3% annually to reflect market conditions. The loan term is 20 years and payments are made monthly. What is the monthly payment after interest rate resets to 3%?

Please show work!

Answer 1

When interest rate is 6%

PV = $26,000, N = 20*12 = 240 months, r = 6/12 = 0.5%, FV = 0

PV = (PMT/r)*[1 – 1/(1+r)^N] + FV/(1+r)^N

26000 = (PMT/0.005)*(1 – 1/1.005^240) + 0

PMT = $186.2721

Monthly payment = $186.2721

Now calculate principal left after 5 years

N = 5*12 = 60 months

26000 = (186.2721/0.003)*(1 – 1/1.003^60) + FV/1.003^60

FV = $18893.93 or $18894

After 5 years, principal left $18894 and interest rate gone down to 3%.

PV = $18894, N = 15*12 = 180 months, FV = 0, r = 3%/12

18894= (PMT/0.003)*(1 – 1/1.003^180) + 0

PMT = $136

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