Question

You buy items costing $3000 and finance the cost with a simple interest fixed installment loan at 5% simple interest per year. The finance charge is $600.a) How many years will you be paying?b) What is your monthly payment?

Answer 1

Given:

The principal amount is P = $3000.

The rate of interest is r = 5% = 0.05.

The interest rate is A = $600.

The objective is,

a) To find the number of years.

b) To find the monthly payment.

Step-by-step explanation:

a)

The general formula for simple interest is,

`A=P* n* r\text{ . . . . . .(1)}`

To find n:

On plugging the given values in equation (1),

`\begin{gathered} 600=3000* n*0.05 \\ n=(600)/(3000*0.05) \\ n=4 \end{gathered}`

b)

Since, the total amount of the item can be calculated as,

`T=A+P\text{ .. . . . (2)}`

On plugging the obtained values in equation (2),

`\begin{gathered} T=600+3000 \\ T=3600 \end{gathered}`

To find monthly payment:

Now, the monthly payment can be calculated as,

`m=(T)/(n*12)\text{ . . . . .(3)}`

Here, m represents the monthly payment, the product of 12 is used to convert the number of years into the number of months.

On plugging the obtained values in equation (3),

`\begin{gathered} m=(3600)/(4*12) \\ m=75 \end{gathered}`

Hence,

a) The number of years is 4 years.

b) The monthly payment is $75.