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# @CPhill @Hecitar

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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.

If I'm being annoying, please don't hesitate to tell me :P

Jun 14, 2017
edited by 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.

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%   Jun 14, 2017