josh has $215 in an account. the interest rate is 14% compounded annually. to the nearest cent, how much…

josh has $215 in an account. the interest rate is 14% compounded annually. to the nearest cent, how much will he have in 3 years? use the formula $b = p(1 + r)^t$, where $b$ is the balance (final amount), $p$ is the principal (starting amount), $r$ is the interest rate expressed as a decimal, and $t$ is the time in years.

josh has $215 in an account. the interest rate is 14% compounded annually. to the nearest cent, how much will he have in 3 years? use the formula $b = p(1 + r)^t$, where $b$ is the balance (final amount), $p$ is the principal (starting amount), $r$ is the interest rate expressed as a decimal, and $t$ is the time in years.

Answer

Explanation:

Step1: Convert interest rate to decimal

Given $r = 14%=0.14$, $p = 215$, $t = 3$.

Step2: Substitute values into formula

$B=p(1 + r)^t=215\times(1 + 0.14)^3$.

Step3: Calculate $(1 + 0.14)^3$

$(1 + 0.14)^3=1.14^3=1.14\times1.14\times1.14 = 1.481544$.

Step4: Calculate final amount

$B=215\times1.481544 = 318.53196\approx318.53$.

Answer:

$318.53$