Question

Suppose P9,500 is invested at 6% interest compounded annually. Approximately how long will it take for the amount in the account to reach P12,000?

Answer 1

P12,000 = P9,500 *1.6X

Answer 2

use
\[ P= P_0 (1.06)^{t} \]
where P is 12000, P0 is 9500 and t is the number of years:
\[ 12000 = 9500 (1.06)^t \]
to solve , divide both sides by 9500
\[ \frac{12000}{9500} = \frac{9500}{9500} (1.06)^t \]
or
\[ 1.06^t = 1.26316 \]
take the log of both sides:
\[ \log(1.06^t) = \log(1.26316) \]
use the rule
\[ \log(a^b) = b\ \log(a) \]

can you finish ?