Question 1149652
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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] <font color=blue>see note below</font>
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 = <font color=red>587.62</font>


Answer: Victoria's monthly payment is <font color=red size=4>587.62 dollars</font>


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<font color=blue>note:</font>
I'm using the formula mentioned on this page
<a href="https://www.mtgprofessor.com/formulas.htm">https://www.mtgprofessor.com/formulas.htm</a>
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
<a href="https://www.calculator.net/payment-calculator.html">https://www.calculator.net/payment-calculator.html</a>
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.
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