3) A 20 year mortgage set up for uniform monthly payments with 6 percent interest compounded monthly is taken over by a new owner after 8 years. At that time $12,000 is still owed on the principal. What was the amount of the original loan?

Original loan = $16,344.91

Explanation:

No of monthly payments remaining at the end of 8 years = 12* 12 = 144

Monthly rate= 6%/12 = 0.5% = 0.005

Loan balance at the end of year 8 = Present value of remaining 144 monthly payments

Present value of annuity = Annuity amount * {1-(1+r)^-n}/r

$12,000 = Monthly payment * (1-1.005-144)/0.005

$12,000 = Monthly payment * 102.47474

Monthly payments = $12,000/102.47474

Monthly payments = $117.10

Original loan = Present value of 240(20 years *12) monthly payments

Original loan = $117.10*(1-1.005^-240)/0.005

Original loan = $16,344.91

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