Question 1202558
<font color=black size=3>
<font color=red>Answers</font>
(a)  $112.80 per month
(b)  $50.18 more
(c)  He saves $74.64


========================================================================


Work Shown for part (a)


The formula to use is
P = (L*i)/( 1-(1+i)^(-n) )
where,
P = monthly payment
L = loan amount
i = monthly interest rate in decimal form
n = number of months


In this case
L = 1800
i = 0.156/12 = 0.013 exactly
n = 1.5*12 = 18 months


We can now compute the monthly payment.
P = (L*i)/( 1-(1+i)^(-n) )
P = (1800*0.013)/( 1-(1+0.013)^(-18) )
P = 112.801552357259
P = 112.80


Ron's monthly payment is $112.80
It can be verified through use of a calculator such as this
<a href="https://www.calculator.net/loan-calculator.html">https://www.calculator.net/loan-calculator.html</a>


-----------------------


Work Shown for part (b)


If he is required to pay back the loan 6 months early, then the 18 month time frame shrinks to 18-6 = 12 months.


We'll use n = 12 this time but keep the other values the same.


P = (L*i)/( 1-(1+i)^(-n) )
P = (1800*0.013)/( 1-(1+0.013)^(-12) )
P = 162.975019846114
P = 162.98


Ron's monthly payment is now $162.98


Subtract the previous monthly payment to find the increase.
162.98 - 112.80 = 50.18


He must pay $50.18 more per month if he wants to pay the loan back 6 months early.


-----------------------


Work Shown for part (c)


In part (a) we found Ron's monthly payment was $112.80
Over the course of 18 months, he pays back a total of 18*112.80 = 2030.40 dollars.
The interest is 2030.40 - 1800 = 230.40 dollars.


In part (b) we found Ron's monthly payment was $162.98
Over the course of 12 months, he pays back a total of 12*162.98 = 1955.76 dollars.
The interest is 1955.76 - 1800 = 155.76 dollars.


As you can see, Ron paying more per month has the advantage of paying less overall interest.


Subtract the interest amounts to determine how much he saves.
230.40 - 155.76 = 74.64


He would save $74.64 if he pays back the loan 6 months early.
</font>