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%.

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Antoine Rollins

13 August, 18:50

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%.

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Sherlock · Answer 1

Answer: 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