You are considering buying a house for $200,000. You have $40,000 in your bank a
ID: 2383865 • Letter: Y
Question
You are considering buying a house for $200,000. You have $40,000 in your bank account which pays 1% APR compounded monthly. If you contribute 10% of the price of the house as a down payment, the terms of your mortgage will be an original balance of $180,000 to be repaid over 30 years with equal monthly payments calculated based on an APR of 5% compounded monthly. Call this loan 1. If you contribute 20% of the price of the house as a down payment, the terms of your mortgage will be an original balance of $160,000 to be repaid over 30 years with equal monthly payments calculated based on an APR of 4% compounded monthly. Call this loan 2.
Which loan option should you take ________ (enter loan 1 or loan 2)
How much better is it in present value terms _________? Enter the dollar amount with no commas or dollar sign, for example 45784
Explanation / Answer
Loan 1:
EMI = P×r×(1 + r)n/((1 + r)n – 1)
=[180000×(5%÷12)×(1+(5%÷12))^360÷((1+(5%÷12))^360–1)]*360-180000-{20000[(1+(1%÷12))^360-1]
=160867
Loan 2:
EMI = P×r×(1 + r)n/((1 + r)n – 1)
=[160000×(4%÷12)×(1+(4%÷12))^360÷((1+(4%÷12))^360–1)]*360-160000
=98505.5
Loan 2 will be selected as it has low interest costs.
Loan 2 is better as it has 62,361.5 interest savings than option 1.
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