Question 1192942: Logan is taking out a loan to buy a $4,000 ring for his girlfriend. He has the two finance options listed below. Which option should be choose? Justify your answer by giving the amount of money Logan will save.
Option A: A 5 year loan with a 7% interest rate compounded quarterly.
Option B: An eight year loan with a 5.5% interest rate compounded annually.
Found 2 solutions by Boreal, MathTherapy:
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! A: 4000=Po (1+(.07/4))^20, since there will be 20 separate times for compounding
4000=Po*1.414778
Po=$2827.30, amount of loan
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B. 4000/(1.055)^8=$2606.39
The loan in B is smaller by about $220. He will save money on the front end but will be paying interest three years longer.
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website!
Logan is taking out a loan to buy a $4,000 ring for his girlfriend. He has the two finance options listed below. Which option should be choose? Justify your answer by giving the amount of money Logan will save.
Option A: A 5 year loan with a 7% interest rate compounded quarterly.
Option B: An eight year loan with a 5.5% interest rate compounded annually.
Option A
A $4,000 loan, paid over a 5-year period, at a 7% quarterly compounded rate results in a $238.76 quarterly payment.
That quarterly payment, for 5 years will amount to 20 periods/payments, or a total payment of $4,775.20.
Option B
A $4,000 loan, paid over an 8-year period, at a 5.5% annually compounded rate results in a $631.46 annual payment.
That annual payment, for 8 years will amount to 8 periods/payments, or a total payment of $5,051.68.
Why don't you do the comparison, decide which offer is better, choose that one, justify your choice, and then calculate the amount he'd save.
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