Caleb purchased his first home for $420,000. He made a 10% down payment and financed the remaining purchase price. The terms of the loan were as follows: 30 year loan Payments made monthly Interest charged at 9% convertible monthly In which month is the first payment for which the principal component is greater than half of the payment?

In 269th Payment the principal component is greater than half of the payment

Explanation:

Amortization schedule is attached please find it.

The loan payment includes the interest and principal portion. After deducting the interest on the due balance the residual amount is paid towards the principal.  

Loan is paid per month, the amount of each payment can be calculated as follow:

Loan Payment per month = r ( PV ) / 1 - ( 1 + r )^-n

r = rate per period = 9% per year = 0.75% per month

n = number months = 30 years x 12 months per year = 360 Months

PV =  present value of all payments = $420,000

P = payment per month = ?

P = 0.75% ( $420,000 x 90% ) / 1 - ( 1 + 0.75% )^-360

P = $3,041.47 per month

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