Question

1. Calculate the mortgage balance after 10 years if the initial mortgage is $1,500,000, with an interest rate of 12% and a 20-year amortization.
2. Provide steps, explanations & formulas used

Answer 1

[NOTE: It is assumed that repayment of loan is yearly]

Present value of annuity = P*[1 - (1+r)^-n / r]

p = annual payments of loan

r = rate of interest

n = number of periods

1,500,000 = P*[1 - (1+12%)^-20 / 12%]

P = 1,500,000 / 7.469443624

P = 200,818.17

Loan balance after 10 years:

remaining period after 10years = 10

using the same above formula

balance loan = 200818.17*[1 - (1+12%)^-10 / 12% ]

loan balance = 200,818.17 * 5.650223

= $1,134,667.45

(NOTE : if the repayments are not yearly then answer would be different]