What is the remaining balance on a 30-year, $400,000 mortgage after 70 months? Assume monthly payments and a nominal rate (monthly compounding) of 5.90%.

The loan balance after 70 months will be $ 366184.45

Explanation:

r = 0.059/12

Present Value (Pv) = 400000

n = 30 x 12 = 360

Monthly Payments = rPv/(1 - (1+r)^-n)

Monthly Repayments = (0.059/12) x 400000/(1 - (1+0.059/12)^-360)

Monthly Repayments = 1966.66664/0.828926661 = 2372.5460074

Monthly Repayments = 2372.55

Loan Balance = PV(1+r)^n - P((1+r)^n - 1)/r

      = 400000(1+0.059/12)^70 - 2372.55((1+0.059/12)^360 -1)/0.059/12

      = 563849.79539 - 197665.34102 = 366184.4543

The loan balance after 70 months will be $ 366184.45

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