MATH SOLVE

4 months ago

Q:
# The sum of $3,000 is deposited into an account paying 10% annually. If $1,206 is withdrawn at the end of years 1 and 2, how much then remains in the account?"

Accepted Solution

A:

What we have so far:

INITIAL CASH AMOUNT IN THE BANK: USD3,000

ANNUAL INCREASE OF THE CASH AMOUNT IN THE BANK: 10%

YEARS THE CASH STAYED IN THE BANK: 2 years.

AMOUNT WITHDRAWN AT THE END OF YEAR 1: USD1,206

AMOUNT WITHDRAWN AT THE END OF YEAR 2: USD1,206

First, we need to solve for YEAR 1:

FOR YEAR 1:

Initial Deposit * Annual Increase Rate = Annual Increase

3,000 * 0.10 = Year 1's Annual Increase

Year 1's Annual Increase = USD300

∴The YEAR 1'S ANNUAL INCREASE IS USD300.

∴The NEW AMOUNT is now USD3,300.

BUT NOT SO FAST! After the year, you took out USD1,206.

New Amount - USD1,206 = Year 1 Amount

3,300 - 1,206 = Year 1 Amount

Year 1 Amount = USD2094

∴The YEAR 1 AMOUNT which will carry over to YEAR 2 is USD2094.

Now, let us solve for the REMAINING BALANCE.

FOR YEAR 2's Annual Increase:

YEAR 1 AMOUNT * Annual Increase = Year 2's Annual Increase

2094*0.10 = Year 2's Annual Increase

Year 2's Annual Increase = USD209.4

∴The YEAR 1'S ANNUAL INCREASE IS USD209.4.

∴The NEW AMOUNT is now USD2,303.4.

But you took out USD1,206

USD2,303.4 - USD1,206 = Remaining Balance

Remaining Balance = USD1097.4

∴The Answer is: USD1097.4

INITIAL CASH AMOUNT IN THE BANK: USD3,000

ANNUAL INCREASE OF THE CASH AMOUNT IN THE BANK: 10%

YEARS THE CASH STAYED IN THE BANK: 2 years.

AMOUNT WITHDRAWN AT THE END OF YEAR 1: USD1,206

AMOUNT WITHDRAWN AT THE END OF YEAR 2: USD1,206

First, we need to solve for YEAR 1:

FOR YEAR 1:

Initial Deposit * Annual Increase Rate = Annual Increase

3,000 * 0.10 = Year 1's Annual Increase

Year 1's Annual Increase = USD300

∴The YEAR 1'S ANNUAL INCREASE IS USD300.

∴The NEW AMOUNT is now USD3,300.

BUT NOT SO FAST! After the year, you took out USD1,206.

New Amount - USD1,206 = Year 1 Amount

3,300 - 1,206 = Year 1 Amount

Year 1 Amount = USD2094

∴The YEAR 1 AMOUNT which will carry over to YEAR 2 is USD2094.

Now, let us solve for the REMAINING BALANCE.

FOR YEAR 2's Annual Increase:

YEAR 1 AMOUNT * Annual Increase = Year 2's Annual Increase

2094*0.10 = Year 2's Annual Increase

Year 2's Annual Increase = USD209.4

∴The YEAR 1'S ANNUAL INCREASE IS USD209.4.

∴The NEW AMOUNT is now USD2,303.4.

But you took out USD1,206

USD2,303.4 - USD1,206 = Remaining Balance

Remaining Balance = USD1097.4

∴The Answer is: USD1097.4