Optimizing Loan Interest Rates: Solving for Loan Length

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SUMMARY

The discussion focuses on optimizing loan interest rates by analyzing two loan offers: \$10,080 at 10% interest for a shorter duration and \$7,000 at 12% interest for a longer duration. The key equation derived is based on the assumption of simple interest, where the time for the \$10,080 loan is 6 months shorter than that for the \$7,000 loan. The equation formulated is (n - 0.5) * (10,080 * 0.10) = n * (7,000 * 0.12), which allows for the calculation of the loan lengths. The problem emphasizes the need for clarity on whether the interest is simple or compound.

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  • Learn how to solve equations involving simple interest
  • Research the differences between simple and compound interest
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Finance students, loan officers, and anyone involved in personal finance or lending practices will benefit from this discussion.

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The problem: Lending companies often offer better rates when you borrow a larger sum of money for a shorter period of time. A borrower is offered a loan of \$10,080 at 10% and a loan of \$7000 at 12%. If the larger loan is 6 mo shorter but the total interest payed is the same, find the length of each loan. (End of problem.) I am trying to write an equation for t (time) but have not been able to solve it. Thanks in advance!
 
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MisterMeister said:
The problem: Lending companies often offer better rates when you borrow a larger sum of money for a shorter period of time. A borrower is offered a loan of \$10,080 at 10% and a loan of \$7000 at 12%. If the larger loan is 6 mo shorter but the total interest payed is the same, find the length of each loan. (End of problem.) I am trying to write an equation for t (time) but have not been able to solve it. Thanks in advance!
Looks like we need to assume that these are single payment loans,
and that simple interest is involved (no compounding).

n = number of years (7000 loan)
n - .5 = number of years (10080 loan)

(n - .5)*(10080*.10) = n*7000*.12

I'll let you finish that off...
 
Is this simple interest or compound interest? If compound interest, how often compounded?
 

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