Question

You are planning to buy a house today. The house costs $400000. You have $57000 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 annual payments and has an EAR of 8% per year. What will be your annual mortgage​ payment?

Answer 1

These can be of two types:

· Ordinary Annuity – payment is made at the end of each period.

· Annuity Due – Payment is made at the beginning of each period

The present value of an Ordinary Annuity can be calculated as:

Where C denotes the fixed installment

r denotes the rate of interest, 8% annually

n denotes the number of installments or 30

The PV of the annuity is the amount of loan borrowed = $ 400,000 - $ 57,000 = $ 343,000

Substituting the above values, calculate C:

Thus, the annual mortgage payment will be $ 30,467.81