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.
Explanation:
a)
The general formula for simple interest is,
[tex]A=P\times n\times r\text{ . . . . . .(1)}[/tex]To find n:
On plugging the given values in equation (1),
[tex]\begin{gathered} 600=3000\times n\times0.05 \\ n=\frac{600}{3000\times0.05} \\ n=4 \end{gathered}[/tex]b)
Since, the total amount of the item can be calculated as,
[tex]T=A+P\text{ .. . . . (2)}[/tex]On plugging the obtained values in equation (2),
[tex]\begin{gathered} T=600+3000 \\ T=3600 \end{gathered}[/tex]To find monthly payment:
Now, the monthly payment can be calculated as,
[tex]m=\frac{T}{n\times12}\text{ . . . . .(3)}[/tex]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),
[tex]\begin{gathered} m=\frac{3600}{4\times12} \\ m=75 \end{gathered}[/tex]Hence,
a) The number of years is 4 years.
b) The monthly payment is $75.
