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)

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

Step-by-step 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 =

or, $ 125 =

or. 125 × 100 = 10,000 × 5 × T

or, T =

or, T =

∴ 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

(a) {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …}

(b) $59 398

step-by-step explanation:

(a) the annual sequence of profits

aₙ = a₁rⁿ⁻¹

the model for the sequence of profits is {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …} .

(b) profit after 15 yr

  a₁ = $ 30 000

  r = 1.05

a₁₅ = 30 000 × 1.05¹⁴

a₁₅ = 30 000 × 1.979 93

a₁₅ = $59 398

the profit in year 15 will be $59 398.