What interest rate will cause $6000 to grow to $6741.60 in 2 years?

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The formula A=P1+r2 gives the amount A in dollars that P dollars will grow to in 2 years at interest rate r where r is given as a decimal), using compound interest. What interest rate will cause $6000 to grow to $6741.60 in 2 years?

Jun 14th, 2015

Thank you for the opportunity to help you with your question!

Ok Let me make it simpler for you.

This is how we write it

P = principal amount (the initial amount you borrow or deposit)

r  = annual rate of interest (as a decimal)

t  = number of years the amount is deposited or borrowed for.

A = amount of money accumulated after n years, including interest.

n  =  number of times the interest is compounded per year 

The  formula is

A= P(1 +r/n) ^nt

$6741.60= $6000(1 +r/1) ^1 x 2


$6741.60=$6000 (1+r) (1+r)

$6741.60=$6000 (1+2r+r^2)

Evaluate the RHS

$6741.60=$6000+$12000r +$6000r^2

Subtract $6000 both sides

$741.6=$12000r +$6000r^2

Solve by completing the square

Which 2 numbers do you add to get 12000 and multiply to get 6000

Am still working on the last part Please give me a few minutes you will have the remaining part

Please let me know if you need any clarification. I'm always happy to answer your questions.
Jun 14th, 2015

Wow!  Great, thank you so much.  Please let me know the remaining part.  Thank you so much!

Jun 14th, 2015

Lets do shorter method at this point

$6741.60=$6000 (1+2r+r^2)

we divide both sides by $6000

1+2r +r^2=$6741.60/$6000

Solving the equation gives using perfect squares

(1+r)(1+r)= 1.1236 

1 +r=1.1236


Changing it a percentage


Jun 14th, 2015

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