Zoe X. answered • 02/10/15
Tutor
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Zoe - Pre-calculus, Calculus, Algebra I & II
Is this question assuming that you start your payment after graduating from college? And are we assuming that you are borrowing at the start of the first year of college?
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Sorry, the site seems to have ate up my response once I hit the 'Save' button. :/
We borrow $20,000 at time 0, and have to pay back the loan with monthly payments starting at the end of the 1st month. We pay back over the course of 10 years. So we make 10 * 12 = 120 monthly payments. The annual rate is given as 4.5%, so the monthly rate is 4.5%/12 = 0.375% = 0.00375.
The loan value is equal to the present value of all these monthly payments.
$20,000 = pmt/(1.00375) + pmt/(1.00375)2 + ... + pmt/(1.00375)120
Obviously this is hard to solve by hand. I use a BA II Plus Professional financial calculator. In the worksheet buttons, I put in these values:
N = 120
I/Y = 0.375 (rate in %)
PV = 20,000
FV = 0 (you're left with balance 0 once you paid it all off)
Then compute PMT (payment).
Let me know how it goes.
Zoe X.
OK.
So we have $20,000 that we borrowed at the beginning. At the end of each month, for 10 years, we make a monthly payment to pay off the loan. So we make a total of 12 * 10 = 120 payments.
The given annual rate is 4.5%. That translates into a monthly rate of (4.5%)/12 = 0.375% = 0.00375
The present value of all the payments equal the value of the loan:
$20,000 = pmt/(1.00375) + pmt/(1.00375)2 + ... + pmt/(1.00375)120
Obviously, you'd likely need a financial calculator to find the payment. Mine is a BA II Plus Professional.
These are the values I put into the Worksheet buttons:
N = 120
I/Y = 0.375 (the monthly rate in %)
PV = 20,000
FV = 0 (at the end you end up with a balance of 0)
Then compute.
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02/12/15
Paul B.
02/11/15