Question 1194152: MAT: Topics in Contemporary Math
Loans
4) How much does college really cost? Suppose the annual tuition for a 4-year college is
$32,000 and fees, books, room and board, and other expenses add an extra $5000 to the
annual cost.
a. What is the total cost of the 4-year education?
b. To pay for this, you take out a loan that charges 4.5% interest and expects to be
paid back in 15 years. What will be your monthly loan payment?
Answer by math_tutor2020(3816)   (Show Source):
You can put this solution on YOUR website!
Part (a)
Tuition costs $32,000 per year. Then there is an extra $5,000 in expenses.
On a yearly basis, the cost of college is $32,000 + $5,000 = $37,000.
Multiply by 4 to get the total cost.
4*37,000 = $148,000
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Part (b)
The monthly payment formula is
P = (L*i)/( 1-(1+i)^(-n) )
where,
P = monthly payment
L = loan amount
i = interest rate per month, in decimal form
n = number of months
In this case,
L = 148,000 dollars
i = 0.045/12 = 0.00375 exactly
n = 15*12 = 180 months (equivalent to 15 years)
Use your calculator to find:
P = (L*i)/( 1-(1+i)^(-n) )
P = (148000*0.00375)/( 1-(1+0.00375)^(-180) )
P = 1,132.19006744392
P = $1,132.19
Some free calculators found online to help check your work
https://www.bankrate.com/loans/loan-calculator/
https://www.calculator.net/loan-calculator.html
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Answers:
(a) $148,000
(b) $1,132.19
You may have to delete the commas if necessary. The same goes for the dollar signs.
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