You deposited $2,000 in a bank account paying 6% on January 1, 2004, and then you made $2,000 deposits on January 1 in 2005 and 2006. Which of the following expressions will calculate your bank balance just after the last payment was deposited?

Question

Quizplus · Accepted Answer

To calculate the bank balance just after the last payment was deposited, we need to calculate the future value (FV) of the initial deposit ($2,000) and the two subsequent deposits ($2,000 each) at the end of three years (i.e., after the 2006 deposit).

We are given that the bank pays 6% interest per year. This means that each year, the investment grows by a factor of 1.06 (i.e., 6% plus 100%).

To calculate the FV of each deposit, we can use the formula:

FV = PV x (1 + r)n

Where PV is the present value (i.e., the amount of the deposit), r is the annual interest rate as a decimal, and n is the number of years.

For the initial deposit made on January 1, 2004, n = 3 (since we want to calculate the FV after three years), r = 0.06 (since the annual interest rate is 6%), and PV = $2,000.

Therefore, the FV of the initial deposit is:

FV1 = $2,000 x (1 + 0.06)3 = $2,437.04

For the two subsequent deposits made on January 1 in 2005 and 2006, n = 2 and 1 respectively (since we want to calculate the FV after two and one years respectively), r = 0.06, and PV = $2,000.

Therefore, the FV of the second deposit is:

FV2 = $2,000 x (1 + 0.06)2 = $2,231.20

And the FV of the third deposit is:

FV3 = $2,000 x (1 + 0.06)1 = $2,120.00

The bank balance just after the last payment was deposited will be the sum of the FVs of all three deposits, i.e.:

FV = FV1 + FV2 + FV3
FV = $2,437.04 + $2,231.20 + $2,120.00
FV = $6,788.24

Therefore, the correct expression to calculate the bank balance just after the last payment was deposited is:

FV = $2,000[1.06]1 + $2,000[1.06]2 + $2,000[1.06]3

which is equivalent to:

FV = $2,231.20 + $2,437.04 + $2,120.00
FV = $6,788.24

You Deposited $2,000 in a Bank Account Paying 6% on January