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
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-> 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
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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?
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
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.
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