Question

rent The compound interest formula is: A = P(1+ P(1+0) where A is the account balance, P is the principal, r is the rate as a decimal, n is the number of compounding periods per year, and t is the time in years. A principal of $2,000 is invested in an account that pays 10% annual interest, and the interest is compounded quarterly. How much is in the account after 5 years? Round your answer to the nearest hundredth.

Answer 1

You have the following formula for the compound interest:

`A=P(1+(r)/(n))^(nt)`

based on the given information you have:

P: principal investment = $2,000

r: rate = 10/100 = 0.1

n: number of compounding periods per year = 4

t: time in years = 5

Replace the previous values of the parameters to calculate the value of the account after 5 years.

`\begin{gathered} A=(2,000)(1+(0.1)/(4))^((4)(5)) \\ A=(2,000)(1.025)^(20) \\ A=3,277.23 \end{gathered}`

Hence, after 5 years the account is $3,277.23