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!

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?

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?

Re: Simple Interest Challenge Problem

Quote:

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...

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?

Re: Simple Interest Challenge Problem

Quote:

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

Re: Simple Interest Challenge Problem

okay thanks Wilmer! I understand it now.

Re: Simple Interest Challenge Problem