You want to buy a house that costs $170,000. You have $17,000 for a down payment
ID: 2668310 • Letter: Y
Question
You want to buy a house that costs $170,000. You have $17,000 for a down payment, but your credit is such that mortgage companies will not lend you the required $153,000. However, the realtor persuades the seller to take a $153,000 mortgage (called a seller take-back mortgage) at a rate of 10%, provided the loan is paid off in full in 3 years. You expect to inherit $170,000 in 3 years, but right now all you have is $17,000, and you can only afford to make payments of no more than $18,000 per year given your salary. (The loan would really call for monthly payments, but assume end-of-year annual payments to simplify things.) Round all answers to the nearest hundredth.
a. If the loan amortized over 3 years, how large would each annual payment be?
What would the loan balance be at the end of Year 3? What would the balloon payment be?
*Please instruct how to derive answer via Financial Calculator! THANKS!!!=0)
Explanation / Answer
After paying 17000 for the down payment, you owe 153000 dollars. Set this as the present value [PV]. If we want to find out how much each annual payment must be if we amortize the loan over 3 years, enter the following keystrokes. As usual I am using a Texas Instruments BA-II Plus so the button symbols may differ slightly. 153000 [PV] 0 [FV] (we want to find out how much each payment needs to be so that we have no remaining debt) 3 [N] 10 [I/Y] [CPT] [PMT] Computing the payment gives us -61523.565 which is a negative value since this is the cash outflow (what we pay). For the second part of the question, we know that since we can only afford to pay 18000 a month, there will be a remaining loan balance at the end of Year 3 that will require a lump balloon payment. With all the previous data still stored on our calculator, we simply enter the following -18000 [PMT] (writing over the previously computer PMT value of -61523.565) [CPT] [FV] which gives us a value of -144063, negative again because this is also a cash outflow (the balloon payment that we must pay).
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