Exercise 16 Page 461

We want to find the amount in a continuously compounded account for the given conditions. Principal:& $500 Annual Interest Rate:& 4.9 % Time:& 2.5 yearsTo do so, we will start by recalling the formula for continuously compounded interest. A( t)= P * e^(r t) In this formula, A( t) represents the amount in the account at time t, P represents the initial value of the account or the principal, r is the annual interest rate, and t is the time in years. Let's substitute the given values into the formula. Note that r should be expressed as a decimal, so 4.9 %=0.049.

A(t)=P* e^(rt)

SubstituteValues

Substitute values

A(t)= 500* e^(0.049( 2.5))

Multiply

Multiply

A(t)=500* e^(0.1225)

CalcPow

Calculate power

A(t)≈ 500* 1.130319120

Multiply

Multiply

A(t)≈ 565.16

The amount after 2.5 years under the given conditions is approximately $ 565.16.