# Thread: Simple Interest Challenge Problem

A father wanted to show his son what it might be like to borrow money from a financial insitution. When his son asked if he could borrow $120 the father lent him the money and setup the following arrangements: He charged his son$6 for the loan of $120. Therefore the son received$114 and agreed to pay his father 12 installments of $10 a month, beginning one month from today,until the loan was repaid. Find the approximate rate of simple interest the father charged on this loan. Please show some work Thanks a ton! 2. ## Re: Simple Interest Challenge Problem That looks like a pretty straight forward problem. He received$114 and payed back $120 over 12 months so the total interest was$6 on $114 for one year. What percent is that? 3. ## Re: Simple Interest Challenge Problem but dont i have to account for the twelve equal payments. wouldnt the$6 dollars interest on $114 (which is 5.3%) be if there was only one payment at the end of 12 months? 4. ## Re: Simple Interest Challenge Problem Originally Posted by thut but dont i have to account for the twelve equal payments. wouldnt the$6 dollars interest on $114 (which is 5.3%) be if there was only one payment at the end of 12 months? You're right. Hallsofivy had too much turkey stuffing! You're asked to "find the approximate rate of simple interest"; I'd do it this way: 114/2 = 57 (approximate average owing) : 6/57 = .10526 ; so 10.53 % You can be a little more precise by taking the 12 monthly balances: 114, 104, 94....14, 4 adding 'em up, divide by 12 for average...won't be much of a difference... 5. ## Re: Simple Interest Challenge Problem Thanks Wilmer! but im a little bit unclear as to why you divide the 114 by 2 to get the approximate average owing? 6. ## Re: Simple Interest Challenge Problem Originally Posted by thut Thanks Wilmer! but im a little bit unclear as to why you divide the 114 by 2 to get the approximate average owing? The$114 is owing at beginning of year...gradually reduces to zero OVER A YEAR: so approximately half is
owing on average.
Take a simpler case: 300, reducing by 100:
300
200
100
===
600
600 / 3 = 200 average

7. ## Re: Simple Interest Challenge Problem

okay thanks Wilmer! I understand it now.