mateo and his cousins are saving to purchase an avocado farm. they invest $25,000 in an account earning 8%…
mateo and his cousins are saving to purchase an avocado farm. they invest $25,000 in an account earning 8% interest each year. mateo thinks the equation below can be used to determine how much money, y, they will have in the account after investing for x years. is mateos equation correct? use the drop - down menus to explain. y = 25,000(0.08)^x click the arrows to choose an answer from each menu. the amount of money in the account after 1 year can be determined by evaluating the expression choose... . the amount of money, y, in the account after x years can be calculated using the equation choose... . mateos equation choose... correct.
Answer
Explanation:
Step1: Recall compound - interest formula
The formula for compound - interest when compounded annually is $A = P(1 + r)^t$, where $P$ is the principal amount, $r$ is the annual interest rate (as a decimal), and $t$ is the number of years. Here, $P=$25000$, $r = 0.08$, and $t=x$.
Step2: Determine the correct formula
The amount $y$ in the account after $x$ years should be $y=25000(1 + 0.08)^x=25000(1.08)^x$.
Step3: Evaluate Mateo's formula
Mateo's formula is $y = 25000(0.08)^x$. This is incorrect because in the compound - interest formula, the base of the exponent should be $1 + r$ (the growth factor), not just $r$.
Answer:
The amount of money in the account after 1 year can be determined by evaluating the expression $25000(1.08)^1$. The amount of money, $y$, in the account after $x$ years can be calculated using the equation $y = 25000(1.08)^x$. Mateo's equation is not correct.