question 1 of 10\nif $1,000 is invested in an account that pays 5% interest compounded annually, an…

question 1 of 10\nif $1,000 is invested in an account that pays 5% interest compounded annually, an expression that represents the amount in the account at end of five years can be given by which of the following equations?\na. $1000(1.05)^5$\nb. $1000(0.5)^5$\nc. $1000+(0.5)^5$

question 1 of 10\nif $1,000 is invested in an account that pays 5% interest compounded annually, an expression that represents the amount in the account at end of five years can be given by which of the following equations?\na. $1000(1.05)^5$\nb. $1000(0.5)^5$\nc. $1000+(0.5)^5$

Answer

Explanation:

Step1: Recall compound - interest formula

The compound - interest formula is $A = P(1 + r)^n$, where $A$ is the amount of money accumulated after $n$ years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (in decimal form), and $n$ is the number of years the money is invested for.

Step2: Identify the values of $P$, $r$, and $n$

Given that $P=$1000$, $r = 5%=0.05$, and $n = 5$ years.

Step3: Substitute the values into the formula

Substitute $P = 1000$, $r=0.05$, and $n = 5$ into the formula $A = P(1 + r)^n$. We get $A=1000(1 + 0.05)^5=1000(1.05)^5$.

Answer:

A. $1000(1.05)^5$