You have just deposited $5,000 into an account that pays 8% after taxes. If you make no additional contributions. How much more will your account be worth when you retire in 40 years than it would be if you waited 10 years before making this deposit?

Question

​You have just deposited $5,000 into an account that pays 8% after taxes. If you make no additional contributions. How much more will your account be worth when you retire in 40 years than it would be if you waited 10 years before making this deposit?

Quizplus · Accepted Answer

This problem involves calculating the future value of a lump sum investment, taking into account the time value of money and the effects of compounding interest. To calculate the future value of the $5,000 investment after 40 years, we can use the formula FV = PV x (1 + r)^n, where PV is the present value of the investment, r is the annual interest rate (after taxes), and n is the number of compounding periods (i.e. years). Using these values, we get:

FV = $5,000 x (1 + 0.08)^40
FV = $5,000 x 21.725
FV = $108,625

To calculate the future value of the investment if we wait 10 years before making the deposit, we need to first calculate the future value of the $5,000 over that 10-year period, then add that amount to the future value calculated above. Using the same formula as before, but with n = 10, we get:

FV1 = $5,000 x (1 + 0.08)^10
FV1 = $5,000 x 2.159
FV1 = $10,797

To find the total future value of the investment, we need to add FV1 to FV:

Total FV = $108,625 + $10,797
Total FV = $119,422

Finally, to find the difference between the two scenarios, we subtract the second future value from the first:

Difference = $108,625 - $119,422
Difference = -$10,797

This means that waiting 10 years before making the deposit actually decreases the future value of the investment by $10,797 compared to making the deposit immediately. Therefore, the best choice is B, $58,309, which is not one of the given options.

​You Have Just Deposited $5,000 into an Account That Pays

You Have Just Deposited $5,000 into an Account That Pays