You are thinking of purchasing a house. The house costs $350,000. You have $50,000 in cash that you can use as a down payment on the house, but you need to borrow the rest of the purchase price. The bank is offering a 30-year mortgage that requires monthly payments and has an APR of 6% per year. What will your monthly payment be if you take this mortgage? how much interest is paid off in your first mortgage payment?

Monthly repayment (P) = $1,798.65

Interest Paid off in First Mortgage = $107,919.09

Explanation:

Monthly repayment (P) = rA / [1 - (1+r) ^-n]

where

A = Loan Amount

r = monthly interest rate

n = loan duration in months

A = House Cost - down payment

= $350,000 - $50,000 = $300,000

r = 6% = 6%/12 = 0.005

n = 30-years = 30 x 12 = 360 months

Monthly repayment (P) = 0.005 ($300,000) / [1 - (1+0.005) ^-360]

Monthly repayment (P) = $1,500 / [1 - (1.005) ^-360]

Monthly repayment (P) = $1,500 / [1 - 0.166041928]

Monthly repayment (P) = $1,500 / 0.833958072

Monthly repayment (P) = $1,798.651575

Monthly repayment (P) = $1,798.65

To Calculate Interest Paid off in First Mortgage Payment

if there is no down payment

Loan Amoun will be $350,000

Monthly repayment (P) = rA / [1 - (1+r) ^-n]

Monthly repayment (P) = 0.005 ($350,000) / [1 - (1+0.005) ^-360]

Monthly repayment P) = $1,750 / [1 - (1.005) ^-360]

Monthly repayment (P) = $1,750 / [1 - 0.166041928]

Monthly repayment (P) = $1,750 / 0.833958072

Monthly repayment (P) = $2,098.426838

Monthly repayment (P) = $2,098.43

Total Payment if loan is $350,000 = $2,098.426838 x 360 = $755,433.6617

Total Payment if loan is $300,000 = $1,798.651575 x 360 = $647,514.5670

Interest Paid off in First Mortgage

Payment = $755,433.6617 - $647,514.5670 = $107,919.0947

= $107,919.09