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Question 912624: I have a student loan totaling $30,000, the APR is 6% and the loan term is 10 years long, what will my monthly payments be, how much will I end up paying over the lifetime of this loan and what will the total interest be that I will have to pay on the loan?
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! The formula to find the monthly payment for any amortized loan is
P = L[c(1 + c)^n]/[(1 + c)^n - 1]
Note: "amortized" is a fancy way of saying "spread out the payments to be paid back over time"
where,
P = monthly payment
L = loan amount (how much the bank gives you). This is the principal
c = monthly interest rate
n = number of payments (each payment occurring monthly)
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Monthly interest rate: c = (yearly rate)/(12 months per year) = r/12 = 0.06/12 = 0.005
Number of payments: n = (number of years)*(12 months per year) = 10*12 = 120
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So in this case,
P = unknown (we're solving for this)
L = 30,000
c = 0.005
n = 120
Plug the values L = 30000, c = 0.005 and n = 120 into the formula to get
P = 30000[0.005(1 + 0.005)^120]/[(1 + 0.005)^120 - 1]
P = 30000[0.005(1.005)^120]/[(1.005)^120 - 1]
P = 30000[0.005(1.81939673403229)]/[1.81939673403229 - 1]
P = 30000(0.00909698367016145)/(1.81939673403229 - 1)
P = 30000(0.00909698367016145)/(0.81939673403229)
P = 30000(0.0111020501941651)
P = 333.061505824954
P = 333.06
So your monthly payment is $333.06
That formula is often a pain to work by hand, which is why calculators like this one:
http://www.bankrate.com/calculators/mortgages/mortgage-calculator.aspx
are handy. Yes it does say "mortgage", but you can apply this calculator to any amortized loan (mortgage, car loan, student loan, etc). Despite having a calculator like this, it helps to know the formula and how to work it by hand.
You will make 120 of these payments (same payment each time), so you will pay a total of 120*333.06 = 39,967.20 dollars
That figure of 39,967.20 includes both the principal of $30,000 and extra interest you pay back.
Total Interest = (Total Paid Back) - (Principal)
Total Interest = (39,967.20) - (30,000)
Total Interest = 9,967.20 dollars
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Summary:
Monthly Payment = $333.06
Total Amount Paid Over Lifetime of Loan = $39,967.20
Total Interest (and Interest Alone) Paid Back = $9,967.20
Note: this is not including any penalty fees you may incur throughout the life of the loan
Let me know if you need more help or if you need me to explain a step in more detail.
Feel free to email me at jim_thompson5910@hotmail.com
or you can visit my website here: http://www.freewebs.com/jimthompson5910/home.html
Thanks,
Jim
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