Question

With interest rates near an all-time low, a family decides to purchase their dream home. The house will cost $350,000. The family will pay 20% as a down payment, and finance the remaining balance with a 15-year fixed rate mortgage. The mortgage will call for monthly payments at a 4.50% APR.  How much interest is paid on the loan in its first two years?

Answer 1

Solution:

Given:

Cost of House = $ 350,000

Down Payment Amount = 20 % of House’s cost = $ 350,000 × 20 / 100 = $ 70,000

Mortgage Amount or Principal = 80 % of House’s Cost = $ 350,000 × 80 / 100 = $ 280,000

Mortgage Time Period = 15 years

Interest Rate on Mortgage = 4.50 % APR Monthly Payment

To Calculate:

Amount of Interest Paid on the Loan in its first 2 years.

Process: Calculations:

Note: In order to calculate the amount paid on the loan in its first 2 years, first we need to calculate the Monthly Mortgage Payment on Loan.

Step: 1 Calculation of Monthly Mortgage Payment on Loan:

Formula: Monthly Mortgage Payment ‘A’:

A = (P × I) / 1 – ((1 + I) ^-n)

Where:

A = Monthly Payment of Mortgage or Loan

P = Principal Amount Taken as Mortgage

I = Interest Rate Per Month

n= Number of Periods of Loan Repayment.

Here:

Principal Amount, P = $ 280,000

Interest Rate = 4.50 APR (Monthly Payment)

Interest Rate Per Month = 0.0450 / 12 = 0.00375

So, Interest Amount, I = 0.00375

Number of Periods of Loan Repayment Duration in Years = 15 Years

Number of Months Required to Repay Loan = 15 Years × 12 Months = 180 Months (as payments are made on monthly basis)

So, Number of Periods, n= 180 Months

On putting the above values in the following formula, we get

A = ($ 280,000 × 0.00375) / 1 – ((1 + 0.00375) ^-180)

A = $ 1,050 / 1 – ((1.00375) ^-180)

A = $ 1,050 / 1 – (0.5097996211)

A = $ 1,050 / 1 – 0.5097996211

A = $ 1,050 / 0.4902003789

A = $ 2,141.9812084931 ≈ $ 2,141.98

Monthly Mortgage Payments on Loan = $ 2,141.98

Step:2 Calculation of the Amount of Interest Paid on the Loan in its first 2 years:

Formula:

Amount of Interest Paid in first 2 Years = Monthly Mortgage Payments on Loan × Number of Months in 2 Years.

Here:

Monthly Mortgage Payments on Loan = $ 2141.98

Number of Months in the first 2 Years = 24 Months (12 months in a year so 12 × 2 = 24 Months in 2 Years)

On putting these values in the formula, we get,

Amount of Interest Paid in first 2 Years = $ 2,141.98 × 24 = $ 51,407.52

Amount of Interest Paid in first 2 Years = $ 51,407.52

Ans: Amount of Interest Paid in first 2 Years = $ 51,407.52