Question

John wants to invest $10,100.00 at a local bank. The investment will earn an annual percentage rate of 4.5% compounded continuously for 5 years. Unfortunately, a mistake was made and the depoßit was only for $10,000.00. How much money did John lose because of this error? Use A = Pen to calculate the future value of the investment.

A $225.10
B $53,45
CS181.25
DS125.23"

Answer 1

To determine how much money John lost due to the error at an interest rate of 4.5% compounded continuously, calculate the future value of both the intended and actual investments and find the difference. The correct answer is $181.25, which is Option C.

Step-by-step explanation:

John wants to invest money at a local bank which offers an annual percentage rate of 4.5% compounded continuously. The future value A of an investment can be calculated using the formula A = Pert, where P is the principal amount, r is the annual interest rate as a decimal, t is the time in years, and e is the base of the natural logarithm (approximately equal to 2.71828).

First, calculate the future value of the intended investment ($10,100): A = 10100e0.045*5 Then, calculate the future value of the investment that was made erroneously ($10,000): A = 10000e0.045*5 The amount John lost due to the error is the difference between these two future values. Subtract the smaller amount from the larger amount to find the loss. After performing these calculations, it can be concluded that the correct option that represents how much money John lost is Option C: $181.25.

Answer 2

John lost approximately $125.65 due to the error when he invested $10,000 instead of the intended $10,100 with an annual interest rate of 4.5% compounded continuously for 5 years.

Step-by-step explanation:

John is looking to invest money in a bank with a certain annual percentage rate compounded continuously. The difference between what he intended to invest and what was actually invested needs to be calculated to determine how much money John lost due to the mistake. We use the formula for continuous compounding A = Pert, where A is the future value of the investment, P is the principal amount, e is the base of the natural logarithm (approximately equal to 2.71828), r is the annual interest rate (in decimal form), and t is the time in years.

For the intended investment (P = $10,100.00):

• A = $10,100.00 * e0.045 * 5
• A = $10,100.00 * e0.225
• A = $10,100.00 * 1.25233...
• A ≈ $12,648.94 (Future value with intended investment)

For the actual investment (P = $10,000.00):

• A = $10,000.00 * e0.045 * 5
• A = $10,000.00 * e0.225
• A = $10,000.00 * 1.25233...
• A ≈ $12,523.29 (Future value with actual investment)

The difference between the future value of the intended investment and the actual investment is:

• $12,648.94 - $12,523.29 = $125.65

Therefore, the amount of money John lost due to the error is approximately $125.65.