# Simple Interest Challenge Problem

• Oct 7th 2012, 01:58 PM
thut
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.
Thanks a ton!
• Oct 7th 2012, 03:15 PM
HallsofIvy
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?
• Oct 7th 2012, 03:35 PM
thut
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?
• Oct 7th 2012, 04:37 PM
Wilmer
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...
• Oct 8th 2012, 11:37 AM
thut
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?
• Oct 8th 2012, 04:39 PM
Wilmer
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
• Oct 8th 2012, 05:05 PM
thut
Re: Simple Interest Challenge Problem
okay thanks Wilmer! I understand it now.
• Nov 4th 2012, 08:14 PM
akilina123
Re: Simple Interest Challenge Problem