# Time value of money question - PV

Ms. Clara Johnson is buying a house. She expects her budget to allow a monthly payment of \$1500 on a 25-year mortgage with an annual interest rate of 6.8 percent. If Johnson makes a 10 percent down payment, the most she can pay for the house is closest to:

A) \$216,116. B) \$240,129. C) \$264,706.

The way the professor solved this:

B is correct. The consumer’s budget will support a monthly payment of 1,500.

Given a 25 year mortgage at 6.8percent, the loan amount will be \$216,115.8.This is obtained by entering the following values :

N = 300,I= 6.8/12,PMT = 1,500,CPT PV.If she makes a 10% down payment –> 240,129.

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Anyone else notice something wrong with the math?

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I think the math is fine. Can you explain how it is wrong?

I agree that the loan amount is 216,115.

If she pays 10% of that (21,611) then we get a total amount of 237,726.

How do we reach 240,129?

Let P represent the price of the house

P = 0.1 x P + loan

0.9 x P = loan

0.9 x P = 216,116

P = 216,116 / 0.9

P = 240,129

Therefore, the maximum Clara can pay is \$240,129.

“Mmmmmm, something…” - H. Simpson

I agree that the loan amount is 216,115.

If she pays 10% of that (21,611) then we get a total amount of 237,726.

She’s not paying 10% of the loan amount as a down payment; she’s paying 10% of the price as a down payment.

Simplify the complicated side; don't complify the simplicated side.

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Thank you guys!

My pleasure.

Simplify the complicated side; don't complify the simplicated side.

Financial Exam Help 123: The place to get help for the CFA® exams
http://financialexamhelp123.com/