Question 1148818: Delaney took out a $32,000 student loan with a fixed interest rate to pay for college. Delaney did not make payments on her loan for a period of 7 years. After this time period interest had accrued, resulting in the loan balance increasing to $60,000.
What is is the 7-year growth factor for the amount that Delaney owes on the loan?
1.7483
Incorrect
What is the 7-year percent change for the amount that Delaney owes on the loan?
74
Incorrect %
What is is the 1-year growth factor for the amount that Delaney owes on the loan?
1.81
Incorrect
What is the 1-year percent change for the amount that Delaney owes on the loan?
Incorrect %
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 60,000 / 32,000 = 1.875
that should be your 7 year growth factor.
you multiply 32,000 by 1.875 and you get 60,000.
multiply that by 100 to get the 7 year percent change factor.
that would be 187.5%.
the amount owed grew 187.5%.
the 1 year growth factor would be found as follows, using the general formula for growth of f = p * (1 + r) ^ n
f is the future value.
p is the present value.
r is the interest rate per time period.
n is the number of time periods.
the formula becomes 60,000 = 32,000 * (1 + r) ^ 7
divide both sides of this formula by 32,000 to get:
60,000 / 32,000 = (1 + r) ^ 7
simplify to get:
1.875 = (1 + r) ^ 7
the 1.875 is your growth factor.
take the 7th root of each side of that equation to get:
1.875 ^ (1/7) = 1 + r
solve for 1 + r to get:
1 + r = 1.093956824.
that's your 1 year growth factor.
32,000 grows by that factor each year for 7 years to get:
32,000 * 1.093956824 ^ 7 = 60,000.
multiply that by 100 to get the 1 year percent change of 109.3956824%.
your answers could be:
1.875
187.5%
1.093956824
109.3956824%
or they could be:
.875
87.5%
.093956824
9.3956824%
it all depends on what they mean by a growth factor or a growth percent.
for example:
it's true that 32,000 * 1.875 = 60,000
you can also say that 32,000 grow by a factor of .875.
in that case you would mean that you multiply 32,000 by .875 and then add that to the original amount to get 60,000.
32,000 * .875 = 28,000 + 32,000 = 60,000
32,000 * 1.875 is equivalent to 32,000 * (1 + .875) which is equivalent to 32,000 * 1 + 32,000 * .875.
the growth factor could be viewed as 1.875 or it could be viewed as .875.
same goes for the growth percent.
i said it was 187.5%.
it could be viewed as .875 * 100 = 87.5%.
same goes for the 1 year growth factor.
it could be viewed as 1.093956824 or it could be viewed as .093956824.
60,000 = 32,000 * 1.093956824 ^ 7 is equivalent to 32,000 * (1 + .093956824) ^ 7
after you divide both sides of that equation by 32,000, and, when you take the seventh root of both sides of that equation, you get:
(60,000 / 32,000) ^ (1/7) = (1 + r)
you then solve for (1 + r) = 1.093956824.
you then subtract 1 from both sides of that equation to get:
r = .093956824.
that is the annual rate of growth.
if they're looking for the growth factor and the percent change as you had shown them, then the third possible set of answers would be:
1.875
87.5%
1.093956824
9.3956824%.
you would round as required.
give it a shot and see how it goes.
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