SOLUTION: Victoria graduates college with 38000 in student loans. if the bank charges 3.6% interest, compounded monthly, and the plan is to pay off the loans in 6 years, how big are the Vict

Algebra ->  Finance -> SOLUTION: Victoria graduates college with 38000 in student loans. if the bank charges 3.6% interest, compounded monthly, and the plan is to pay off the loans in 6 years, how big are the Vict      Log On


   

Question 1149652: Victoria graduates college with 38000 in student loans. if the bank charges 3.6% interest, compounded monthly, and the plan is to pay off the loans in 6 years, how big are the Victoria's payments?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

L = loan amount = 38000
r = annual interest rate in decimal form = 0.036
c = interest rate per period in decimal form = r/12 = 0.036/12 = 0.003
y = number of years = 6
n = number of periods = number of months = y*12 = 6*12 = 72

P = monthly payment
P = L[c(1 + c)^n]/[(1 + c)^n - 1] see note below
P = 38000[0.003(1 + 0.003)^72]/[(1 + 0.003)^72 - 1]
P = 38000[0.003(1.003)^72]/[(1.003)^72 - 1]
P = 38000[0.003(1.24070112913527)]/[1.24070112913527 - 1]
P = 38000(0.00372210338740582)/(1.24070112913527 - 1)
P = 38000(0.00372210338740582)/(0.240701129135273)
P = 38000(0.0154635892269288)
P = 587.616390623296
P = 587.62

Answer: Victoria's monthly payment is 587.62 dollars

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note:
I'm using the formula mentioned on this page
https://www.mtgprofessor.com/formulas.htm
Though the page talks about mortgage payments, the idea applies to any loan in which you pay the balance off monthly, and compound interest is involved (compounding monthly).

Another handy reference is this monthly payment calculator
https://www.calculator.net/payment-calculator.html
which not only computes the monthly payment, but it also shows the monthly amortization schedule. This schedule is a table showing what your interest payment, principal payment and balance will be for any given month.