Gayle has money invested in an account. After 6 years, compounded monthly, she will have $6044.34 in her account, $1344.34 of which is earned interest. What is the interest rate of Gayle’s account? Round your answer to two decimal places.

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Julius
Jun 14, 2017

#1**+2 **

$6,044.34 - $1,344.34 =$4,700 amount invested.

$6,044.34/4,700 =1.28603.......

1.28603^(1/72) =1.0035

1.0035 -1 =0.0035 Interest rate per month.

0.0035 x 1200 = 4.20% annual interest rate compounded monthly.

Guest Jun 14, 2017

#2**+1 **

The principal, P, must have been

Ending Amount - Interest Earned =

$6044.34 - $1344.34 = $4700

We can find the interest rate, r, thusly :

$6044.34 = $4700 ( 1 + r/12)^(12 * 6)

$6044.34 = $4700 ( 1 + r/12)^(72 ) divide both sides by $4700

6044.34 / 4700 = ( 1 + r/12)^(72 ) take the log of both sides

log ( 6044.34 / 4700 ) = log ( 1 + r/12)^(72 ) and we can write

log ( 6044.34 / 4700 ) = 72 * log ( 1 + r/12) divide both sides by 72

log ( 6044.34 / 4700 ) / 72 = log ( 1 + r/12)

0.00151738 = log ( 1 + r/12) and we can write

10^ (0.00151738) = ( 1 + r/12) subtract 1 from both sides

10^ (0.00151738) - 1 = r/12

0.00350001 = r/12 multiply both sides by 12

.042 = r = 4.2%

CPhill
Jun 14, 2017