Question

A radio commercial for a loan company states: “You only pay $0.29 a day for. each $500 borrowed.” If you borrow $1,500 for 120 days, what amount will you. repay, and what annual interest rate is the company actually charging?

Answer 1

Total amount to be repay is $ 1604.4

The annual interest rate the company actually charging is 25.40%

Explanation:

Given: A radio commercial for a loan company states: “You only pay $0.29 a day for each $500 borrowed.” We have borrowed $1,500 for 120 days.

We have to determine the amount to be repay and the annual interest rate the company actually charging.

UNITARY method is a method in which we first find the value of a single unit and then find the desired value by multiply it with unit value.

Since, we have to pay $0.29 a day for each $500 borrowed.

Thus, when we borrow $1 , we pay
`(0.29)/(500)`

So, when $1500 is borrowed , we pay
`(0.29)/(500)* 1500=0.87`

Thus, for 120 days we pay 0.87 × 120 = $104.4

Thus, total amount to be repay = 1500 + 104.4 = $ 1604.4

and annual interest rate is given by,

`SI ={P* r* t}`

We have to find rate

Simple interest = $ 104.4

Principal = $1500

time = 120 days

In year time is
`(120)/(365)`

Substitute, we have,

`104.4=(1500* r* 120)/(365)`

Simplify, we have,

r = 25.40%

Thus, the annual interest rate the company actually charging is 25.40%

Answer 2

Total Interest will be = .29*1500*12 / 500 = 104.4
so total amount to be repay = 1500+104.4=1604.4
and annual interest rate = 104.4*100*360/1500*120=20.88%
hope it helps