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An account with the amount an initial amount of $B earns compound interest at an annual effective interest rate i. The interest in the third year is $426 and the discount in the seventh year is $812. Find i.

Respuesta :

Answer:

rate = 17.49 %

Explanation:

given data

initial amount = $B

annual effective interest rate =  i

interest in the third year =  $426

discount in the seventh year = $812

solution

we know here formula for interest rate that is

interest = initial amount × [tex](1+r)^{t}[/tex]    .............1

$426 = $B × [tex](1+r)^{t}[/tex]

$B  = [tex]\frac{426}{(1+r)^3}[/tex]  ...............2

$812 = $B × [tex](1+r)^{t}[/tex]  

$B  = [tex]\frac{812}{(1+r)^7}[/tex]   ...............3

so from equation 2 and 3 we compare initial amount

[tex]\frac{426}{(1+r)^3} = \frac{812}{(1+r)^7}[/tex]  

solve it we get t

rate r  = 0.1749

rate = 17.49 %

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