Calculate the amount of interest paid for each option and how much does the buyer save with the 20 year option in the following case:
The price of small cabin is 50000. The banks require 5% down payment and the buyer is offered two mortgage options: 20 years fixed at 9.5% or 30 years fixed at 9.5%.
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The formula for the monthly payment to be made for a mortgage is given by `M = (P*r*(1 + r)^N)/((1+r)^N - 1)` where r is the monthly rate of interest, N is the tenure in terms of number of months and P is the principle amount. The total interest paid is M*N - P.
It is given that the cabin costs $50000 with a 5% down payment. The mortgage is for $47500.
For the first option with a tenure of 20 years and the interest rate of 9.5%, `M = (47500*(.095/12)*(1+.095/12)^240)/((1+.095/12)^240 - 1)` = 442.76. The total interest paid is 442.76*240 - 47500 = 58762.95
For the second option with a tenure of 30 years and the interest rate of 9.5%, `M = (47500*(.095/12)*(1+.095/12)^360)/((1+.095/12)^360 - 1)` = 399.40. The total interest paid is 399.4*360 - 47500 = 96286.06
With the 20 year mortgage the buyer saves $37523.11
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