# According to the following, how many years until the value of the CD is double the amount originally invested ( round answer to the nearest year?bob invested $1000 in a bank CD. the CD earns 3%...

According to the following, how many years until the value of the CD is double the amount originally invested ( round answer to the nearest year?

bob invested $1000 in a bank CD. the CD earns 3% interest compunded annually. using the formula, A=P(1+r)t, where A = value of CD, P=principle (original) amount invested, r=interest rate (in decimal form), and t=time in years, determine the followingal form), and t=time in years, determine the follow

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A=P (1+r)^t

A = Value of CD

P = original amount= 1000

r = the rate = 3% = 0.03

t= time

We need to find t such that A is doubled

==> A = 2*1000 = 2000

Now we will substitute.

==> 2000 = 1000( 1+0.03)^t

==> 2000= 1000(1.03)^t

Divide by 1000

==> 2= (1.03)^t

Apply logarithm to both sides.

==> log 2 = log (1.03)^t

==> log 2 = t*log (1.03)

==> t= log 2 / log 1.03

==> t= 23.4 years

**Then the time needed if 23 years.**

**** A=P(1+r)^t