Question

1. reasoning a bank manager wants to encourage new customers to open accounts with initial deposits of at least $3,000. he has posters made for the promotion.

a. under the new promotion, what is the minimum amount of interest a new account would make in one year if there were no withdrawals from the account?
b. the manager wants to add the sentence, “open an account with $3,000 and earn at least $120 interest each year!” to the poster. do you agree? explain.

Explanation:

Step1: Recall simple - interest formula

The simple - interest formula is $I = Prt$, where $I$ is the interest, $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the time in years.

Step2: Convert the interest rate to decimal

The annual interest rate $r = 4.8\%=0.048$, the principal amount $P = 3000$, and $t = 1$ year.

Step3: Calculate the minimum interest for part a

Substitute the values into the formula: $I=Prt=3000\times0.048\times1 = 144$.

Step4: Analyze part b

We found that the interest for a $\$3000$ deposit at a $4.8\%$ simple - interest rate for 1 year is $I = 144$. Since $144>120$.

Answer:

a. $\$144$
b. Yes, because when a customer opens an account with $\$3000$ at a $4.8\%$ simple - interest rate, the annual interest is $\$144$ which is more than $\$120$.