ivana has decided to invest some money in a bank that offers continuous compounding interest. how much will…

ivana has decided to invest some money in a bank that offers continuous compounding interest. how much will be in the account after 10 years?\na = pe^{rt}\nprincipal amount (p): $1,000\nannual interest rate (r): 5% or 0.05\ntime (t): 10 years\nenter your answer in the box, rounding to two decimal places.\n$

ivana has decided to invest some money in a bank that offers continuous compounding interest. how much will be in the account after 10 years?\na = pe^{rt}\nprincipal amount (p): $1,000\nannual interest rate (r): 5% or 0.05\ntime (t): 10 years\nenter your answer in the box, rounding to two decimal places.\n$

Answer

Explanation:

Step1: Substitute values into formula

Given (A = Pe^{rt}), (P=$1000), (r = 0.05), (t = 10). Substitute into the formula: (A=1000\times e^{0.05\times10}).

Step2: Calculate the exponent

First calculate (0.05\times10 = 0.5). So the formula becomes (A = 1000\times e^{0.5}).

Step3: Evaluate (e^{0.5})

Using a calculator, (e^{0.5}\approx1.64872).

Step4: Calculate (A)

Multiply (1000\times1.64872 = 1648.72).

Answer:

(1648.72)