Question

Paula Frye loaned $10,000 to her son's new business at 5% ordinary simple interest (360-day year). At the end of the loan period, Paula received the $10,000 plus $125 interest. Compute the length of the loan period (to the nearest day)

Answer 1

The length of the loan period is 0.25 years , i.e 3 months

Explanation:

Given as :

The loan amount = $ 10,000

The rate of interest applied = 5 % at simple interest yearly

The Amount receive = $ 10 ,000 + 125 interest

So, The interest receive for the loan = $ 125

Let the duration of loan period = T years

From Simple Interest method

Simple Interest =
`(\textrm Principal* \textrm rate* \textrm Time)/(100)`

or, $ 125 =
`(\textrm $ 10,000* \textrm 5* \textrm Time)/(100)`

or. 125 × 100 = 10,000 × 5 × T

or, T =
`(125* 100)/(5* 10,000)`

or, T =
`(12500)/(50,000)`

∴ T = 0.25

So, the time period of loan = 0.25 years = 3 months

Hence The length of the loan period is 0.25 years , i.e 3 months Answer