Question

9,100 dollars is placed in a savings account with an annual interest rate of 5%. If no money is added or removed from the account, which equation represents how much will be in the account after 6 years?

1.) M=9,100(1 + 0.05)^6
2.)M=9,100(1 - 0.05)^6
3.)M=9,100(1 + 0.05)(1 + 0.05)(1 + 0.05)
4.)M=9,100(0.95)^6

Answer 1

1.) M=9,100(1 + 0.05)^6

Explanation:

Compound Interest Rate Formula:

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

In this formula the "P" represents the principle amount, or the original amount. The "r" represents the interest rate in decimal form, while the "n" represents the number of compounds in the time unit (usually years), and the "t" represents the amount of time that has passed (usually years)

In this case it says annual interest rate of 5% and nothing of compound monthly, etc... so n=1, and r=0.05. We're also given the principle amount of 9,100 and the time passed is just 6 years, so t=6. Plugging all this information into the equation we get:

`A=9,100(1+0.05)^6`

which makes the first option correct.