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Chapter 3: Problem 3

Josh has a savings account at a bank that charges a \(\$ 10\) fee for every month his balance falls below \(\$ 1,000 .\) His account has a balance of \(\$ 1,203.44\) and he withdraws \(\$ 300 .\) What will his balance be in six months if he makes no deposits or withdrawals?

Short Answer

Expert verified
The balance in Josh's account will be $843.44 after six months if no additional deposits or withdrawals are made.

Step by step solution

01

Withdrawal

Initially, Josh withdraws $300 from his account. Hence, the new balance after withdrawal of $300 from $1,203.44 would be $1,203.44 - $300 = $903.44.
02

Evaluate monthly fee

Since the new balance is lower than $1,000, the bank will charge a $10 fee per month. So, the new balance will decrease by $10 every month.
03

Compute total balance after six months

After 6 months, the amount of total fees will be 6 months * $10/month = $60. The remaining balance in the account will be the new balance after withdrawal subtracted by the total fees, which calculates to be $903.44 - $60 = $843.44.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Savings Account Fee
A savings account fee is a charge imposed by banks when certain conditions aren't met. In Josh's case, his bank charges a fee if his account balance falls below $1,000. This is quite common among banks as it encourages customers to maintain a minimum balance.
To be specific, the fee applied here is $10 per month, but remember that different banks may have different fee structures and amounts.
It's crucial always to understand the terms and conditions of any account agreement to avoid unexpected charges.
Monthly Balance Calculation
Calculating the monthly balance in a savings account requires you to consider both the initial balance and any subsequent changes that occur throughout that month. After Josh's withdrawal, the balance is recalculated as follows:
  • Start with an initial amount.
  • Subtract any withdrawals.
  • Determine if monthly fees are applicable.
The monthly balance affects account fees and determines the amount of available funds for future use.
In our scenario, Josh's balance after the withdrawal was reduced from $1,203.44 to $903.44.
This new balance then influences whether a fee will be applied in the following months.
Withdrawal Impact
Withdrawals directly affect your account balance, sometimes leading to additional charges or consequences.
For Josh, a $300 withdrawal took his balance from $1,203.44 to $903.44. This action not only immediately reduces available funds but also triggered a monthly fee.
To mitigate withdrawal effects, understanding how much money is safe to withdraw without incurring fees or falling below a crucial threshold is essential.
It's best to plan withdrawals carefully to ensure your balance remains healthy, avoiding unexpected fees and keeping future financial goals on track.
Fee Calculation in Algebra
Fee calculations in algebra use simple arithmetic but can have a significant impact over time.
In Josh's case, he needed to calculate the total fees over six months. Here's how it works:
  • Identify the monthly fee amount, in this case, $10.
  • Calculate the fee's total impact over a specific period: 6 months * $10/month = $60.
Algebra aids in simplifying these calculations and helps to forecast future financial scenarios by providing clear, concise results.
Understanding these concepts thoroughly ensures you can handle similar problems accurately and confidently.

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Most popular questions from this chapter

Barbara wants to restore her 66 Mustang in 4 years. She puts \(\$ 200\) into an account every month that pays 4.5\(\%\) interest, compounded monthly. How much is in the account after 4 years?

Beth and Mark would like to put some savings in the bank. They most likely will not need this money for 4 years, so Beth wants to put it in a four-year CD. Mark wants to put the money in a passbook savings account. What is the advantage of a CD? What is the disadvantage?

An elite private college receives large donations from successful alumni. The account that holds these donations has \(\$ 955,000,000\) currently. a. How much would the account earn in one year of simple interest at a rate of 5.33\(\%\) ? b. How much would the account earn in one year at 5.33\(\%\) if the interest was compounded daily? Round to the nearest cent. c. How much more interest is earned by compounded daily as compared to simple interest? d. If the money is used to pay full scholarships, and the price of tuition is \(\$ 61,000\) per year to attend, how many more students can receive full four- year scholarships if the interest was compounded daily rather than using simple interest?

If \(\$ 3,000\) is invested at an interest rate of 4.8\(\%\) , compounded hourly for two years, what is the ending balance?

Lindsay invests \(\$ 80\) in an account that pays 5\(\%\) annual interest, compounded monthly. Michele invests \(\$ 60\) in an account that pays 8\(\%\) annual interest, compounded weekly. a. Whose balance is greater after one year? b. Whose balance is greater after twelve years?
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