victoria invested $9,300 in an account paying an interest rate of 4.5% compounded continuously. assuming no…

victoria invested $9,300 in an account paying an interest rate of 4.5% compounded continuously. assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 7 years?

victoria invested $9,300 in an account paying an interest rate of 4.5% compounded continuously. assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 7 years?

Answer

Explanation:

Step1: Identify the formula

The formula for continuous compounding is ( A = Pe^{rt} ), where ( P ) is the principal amount, ( r ) is the annual interest rate (in decimal), ( t ) is the time in years, and ( A ) is the amount of money accumulated after ( t ) years, including interest.

Step2: Substitute the values

Given ( P=$9300 ), ( r = 4.5%=0.045 ), and ( t = 7 ) years. Substitute these values into the formula: ( A=9300\times e^{0.045\times7} ). First, calculate ( 0.045\times7 = 0.315 ). So, ( A = 9300\times e^{0.315} ).

Step3: Calculate ( e^{0.315} )

Using a calculator, ( e^{0.315}\approx1.37 ) (more accurately, using a calculator with ( e^x ) function: ( e^{0.315}\approx1.370968 )).

Step4: Calculate ( A )

( A=9300\times1.370968 ). ( A = 9300\times1.370968=12740.0024 ).

Answer:

( 12740.00 )