Question 1078701: If P dollars invested in an account that earns interest at 7% compounded annually the amount available after t years is A=P(1+1.07)^t. How many years will it take for $16000 in this account to grow to $22400?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the formula is actually:
A = P * (1 + .07) ^ T
since 1 + .07 is equal to 1.07, the formula becomes:
A = P * 1.07 ^ T
replace P with 16,000 and replace A with 22,400 and the equation becoms:
22,400 = 16,000 * 1.07 ^ T
divide both sides of the equation by 16,000 to get:
22,400 / 16,000 = 1.07 ^ T
simplify to get:
1.4 = 1.07 ^ T
take the log of both sides of the equation to get:
log(1.4) = log(1.07 ^ T)
this is equivalent to:
log(1.4) = T * log(1.07)
divide both sides of the equation by log(1.07) to get:
log(1.4) / log(1.07) = T
solve for T to get T = 4.973085396
16,000 should grow to 22,400 in 4.973085396 years.
to confirm, replace T in the original equation to get:
22,400 = 16,000 * 1.07 ^ (4.973085396)
use your calculator to evalutat 16,000 * 1.07 ^ (4.973085396)
you will find that it is equal to 22,400, confirming the solution is correct.
the peoerty of logs that allows you to solve this equation is:
log(b^x) = x * log(b)
for example:
log(2^5) = 5 * log(2)
use your calculator to get log(2^5) and use your calculator to get 5 * log(2)
both answers should be the same, namely 1.505149978
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