Question

James wants to buy a house worth $1,000,000. To do so, he takes out a mortgage loan equal to the price of the house. The mortgage has to be repaid after 15 years and make monthly payments with an APR of 10%. Given this information, answer the following

(a) 5 points. Draw the timeline that describes all cash flows (paid and received) throughout the duration of the loan. On the timeline, you must also indicate what is the last period/payment! Denote the period cash flow payment as C.

(b) 5 points. How can James calculate what is the payment C he has to make on that loan? (Write down the formula together with all information necessary to calculate the payment C. The final expression should have C on the left side and all other information on the right side of the equation).

Answer 1

First we need to find out the monthly payment:

We are given the following information

Payment	PMT	To be calculated
Rate of interest	r	10.00%
Number of years	n	15.00
Monthly	frequency	12.00
Loan amount	PV	1000000.00

We need to solve the following equation to arrive at the required PMT:

So the monthly payment is 10746.05

To make the time line we have to make an amortization schedule:

Opening balance = previous year's closing balance
Closing balance = Opening balance+Loan-Principal repayment
PMT is calculated as per the above formula
Interest = 0.1 /12 x opening balance
Principal repayment = PMT - Interest
Below is the timeline of interest and principal payment: