SOLUTION: Ron borrowed $1800 to finance a computer at 15.6%/a compounded monthly for 1 1/2 years. a) How much will his monthly payments be? b) How much more would Ron have to pay per month

Question 1202558: Ron borrowed $1800 to finance a computer at 15.6%/a compounded monthly for 1 1/2 years.
a) How much will his monthly payments be?
b) How much more would Ron have to pay per month to pay the loan off 6 months early?
c) How much interest would Ron save if he paid the loan off early?

Found 2 solutions by math_tutor2020, mananth:
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

Answers
(a) $112.80 per month
(b) $50.18 more
(c) He saves $74.64

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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
https://www.calculator.net/loan-calculator.html

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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.

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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.

Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Ron borrowed $1800 Xo
15.6%/a compounded monthly 0.156/12= 0.013 =r

for 1 1/2 years.= 18 months n

Use calculator plug in the values

= $112.80

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