Stephen said that the ratio of his mortgage to the sales price of his house is 7 to 6. Is this reasonable? Explain your answer.
I don't understand how to figure this question out?
I presume that by mortgage here is meant to total value to be paid back for the loan.
When the bank lends you money, you have to pay back more than you borrowed, the extra being the interest.
We don't know how much Stephen borrowed, but we know he has to pay back 7/6 of that amount. Sounds like a good deal to me, given the typical length of a mortgage! Check some mortgage websites to get an idea of typical rates and lengths.
Is is possible to show his interest as a ratio or percentage?
Interest is usually shown as a percentage rate per year, but since we don't know the number of years, we can't calculate it here.
Mortgages are usually for 10-30 years. If it was one year, which would be very very short for a mortgage, the rate would be 1/6, since he has to pay back 1/6 more than he borrowed.
To express 1/6 as a percent, multiply by 100 and call it percent
1/6 = 100/6% = 16.66%
Would it be more effective if we knew the sale price of the house?
I honestly don't get how to answer this question...wouldn't it be up to Stephen if the ratio 7 to 6 is reasonable or not? I don't know how to reply.
No, the sale price of the house doesn't matter. It could be 6,000 or 6,000,000; we don't care for this purpose.
What we know is that for every 6 dollars Stephen borrows, he has to pay 7 back.
What we don't know, that we would like to know, is how long Stephen has to pay it off. If he has to pay it off next week, then that's very high interest, 16% in a week, and quite unreasonable. If he has to pay it off in a century, then the interest is very very low indeed, a small fraction of 1% per year.
A typical mortgage might be 20 years.
At 20 years, he has to pay 7/6 of his price, that's 1/6 interest over 20 years, which is about 0.75% (=(7/6)^(1/20) - 1) which, as I said, looks like a very good deal.
But you're quite right: what Stephen thinks is reasonable is up to Stephen!
To determine if Stephen's statement about the ratio of his mortgage to the sales price of his house is reasonable, we need to compare the given ratio (7 to 6) with commonly accepted ranges for mortgage ratios.
1. Calculate the mortgage ratio: Dividing the numerator (7) by the denominator (6), we get a ratio of 7/6 or approximately 1.17.
2. Determine acceptable mortgage ratios: Generally, a reasonable mortgage ratio is around 28-36% of the sales price of the house.
3. Convert the acceptable range to a ratio: Using the lower end of the acceptable range (28%), we convert it to a ratio by dividing 28 by 100, resulting in a ratio of 0.28.
Now, we can compare the calculated mortgage ratio (1.17) with the acceptable mortgage ratio (0.28).
If the calculated mortgage ratio (1.17) is greater than the acceptable ratio (0.28), it would suggest that Stephen's mortgage is relatively high compared to the sales price of his house, which may raise concerns about affordability.
However, if the calculated mortgage ratio (1.17) is within the acceptable range (less than or equal to 0.28), it would indicate that Stephen's mortgage is reasonable in relation to the sales price of his house.
Therefore, to determine whether Stephen's statement is reasonable or not, compare the calculated mortgage ratio (1.17) with the acceptable mortgage ratio (0.28).