Question

A loan of $1.070 was repaid at the end of 18 months with a check for $1.100 What annual rate of interest was charged?The annual rate of interest was charged at % (Round to two decimal places as needed)

Answer 1

The formula for the simple interest is:

`A=A_0\cdot(1+n\cdot r).`

Where:

• A is the final amount of money after n years,

,

• A0 is the initial amount of money,

• r is the interest rate.

In this problem, we have.

• A = $1100,

,

• A0 = $1070,

,

• n = 1.5 years,

,

• r = ?.

Replacing the data of the problem in the equation above, we have:

`\text{ \$1100 }=\text{ \$1070}(1+1.5\cdot r).`

Solving the last equation for r, we get:

`\begin{gathered} \frac{\text{ \$1100}}{\text{ \$1070}}=1+1.5r, \\ (1100)/(1070)-1=1.5r, \\ r=(1)/(1.5)\cdot((1100)/(1070)-1), \\ r\cong0.0187=1.87\%. \end{gathered}`

Answer

The interest rate was charged at 1.87%.