Question

The amount of interest on $x for 2 years is$320. the amount of discount on $x for one year is $148. find the annual effective interest rate i and the value of x.

Answer 1

The answer is "
`\bold{i=0.05311 \ \ and \ \ x= \$ 2934.4670}`"

Explanation:

2-year interest is:

`\to (x)i + x(1 + i)i=320.......(i)`

The price of the discount is :

`\to x((i)/(1+i))=148......(ii)`

by mixing (ii) in (i), we get:

`\to 148(1+i)+148(1+i)^2=320 \\\\\to (i+1)(i+2)= (320)/(148) \\\\\to i = 0.05311 \\`

`\to`
`x= 148((i+1)/(i)) \\\\`

`= 148(0.054311)+ (1)/((0.005311))\\\\ =$2934.4670`

The Interest rate of annual impact:

i=0.05311

x=$ 2934.4670