Optimizing Loan Interest Rates: Solving for Loan Length

In summary, the problem involves comparing two loans, one for \$10,080 with an interest rate of 10% and one for \$7000 with an interest rate of 12%. The larger loan is 6 months shorter but the total interest paid is the same. The task is to find the length of each loan by writing an equation for time (t). The loans are assumed to be single payment loans and simple interest is involved.
  • #1
MisterMeister
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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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  • #2
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...
 
  • #3
Is this simple interest or compound interest? If compound interest, how often compounded?
 

FAQ: Optimizing Loan Interest Rates: Solving for Loan Length

What are interest rates of loans?

Interest rates of loans refer to the percentage of the loan amount that is charged by the lender for borrowing money. This is essentially the cost of borrowing money and is typically expressed as an annual percentage rate (APR).

How are interest rates of loans determined?

Interest rates of loans are determined by a variety of factors, including the current economic conditions, the borrower's credit score, the type of loan, and the lender's policies. Generally, the higher the perceived risk of default by the borrower, the higher the interest rate will be.

Why do interest rates of loans vary?

Interest rates of loans can vary due to a number of reasons, such as the type of loan, the length of the loan, the borrower's creditworthiness, and the current market conditions. Different lenders may also have different interest rates based on their individual policies and risk assessment.

How do interest rates of loans affect the overall cost of borrowing?

The interest rate of a loan directly affects the overall cost of borrowing money. A higher interest rate means a higher cost of borrowing, while a lower interest rate means a lower cost. It is important to compare interest rates from different lenders to ensure the most affordable option.

Can interest rates of loans change over time?

Yes, interest rates of loans can change over time. They are influenced by various economic factors and can fluctuate based on market conditions. Some loans, such as adjustable-rate mortgages, have interest rates that can change periodically during the loan term.

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