Problem

In February 2009 , President Obama signed into la…

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Problem 54 Easy Difficulty

Colleen and Bill have just purchased a house for $\$ 650,000,$ with the seller holding a second mortgage of $\$ 100,000 .$ They promise to pay the seller $\$ 100,000$ plus all accrued interest 5 years from now. The seller offers them three interest options on the second mortgage:
(a) Simple interest at $12 \%$ per annum
(b) $11 \frac{1}{2} \%$ interest compounded monthly
(c) $11 \frac{1}{4} \%$ interest compounded continuously Which option is best; that is, which results in the least interest on the loan?

Answer

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Chapter 5

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Section 7

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Video Transcript

Alrighty for number 54. We're trying to figure out um if the fires of this house have $100,000, they have to kind of invest in to get the interest figured out how much teachers are going to have to pay for these people to um Be able to sell them by their house or whatever. We have. $100,000 is going to be our principal. We're gonna start with simple interest Hypothetically at a percentage rate of 12% for five years. So we're going to plug it into, I equals $100,000 Times a rate of .12 for five years. That's going to give you interest of 60,000. So when you add that together, your amount is going to be 160,000 at that possibility. But then they give you two other possibilities. The other possibility is what if it's 11.5% or 11.5%? Uh compounded monthly four or 5 years. So we're gonna have our a. Is equal to a principle which is $100,000 Times one plus r. rate a .115 over 12 to the 12 times five power. And so when we do that, you're going to end up getting, you do 0.11 five divided by 12 at one race to the 60th power because 12 times five or 60 And then times about 100,000, you're going to be at $175,505 approximately rounded to the nearest whole dollar. And then for part C they say 11 and 1/4 percent. That's 11.25% rate compounded uh continuously for five years. So we're going to plug in and do a is equal to $100,000 Times E to the rate of .11- five times 5. So you do eat the 0.11 to five times five. Power times that by 100,000 and your calculator, you should end up getting 100 and 75,000. Oops. This one, I apologize, should end up being a little bit higher. It was 177. I looked at the wrong number. 177 to 27. And this one is the 175 505 I apologize. Okay, so when it's asking which one is the better option? Obviously the less amount is good. So the first option of doing simple interest at 12% that

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