Question

In: Finance

James wants to buy a house worth $1,000,000. To do so, he takes out a mortgage...

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).

Solutions

Expert Solution

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:


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