Question

Annual deposits of $3500 are made into an account paying 8 percent interest per year compounded continuously. What is the balance in the account right after and right before the 5th deposit?

A) $23,802.56, $23,315.42
B) $22,000.00, $21,642.87
C) $20,680.32, $20,250.00
D) $18,332.89, $17,968.24

Answer 1

To determine the balance in the account immediately after and right before the 5th deposit, the future value of each deposit is calculated using the formula for continuous compounding and then summed up. The balance before the 5th deposit is the total of these calculated amounts, and after the deposit, the deposit amount is added to the total.

Step-by-step explanation:

The question is asking to calculate the balance in a bank account after making annual deposits in an account paying a percent interest per year compounded continuously. We use the formula for continuous compounding which is A = Pert, where P is the principal amount (the initial amount of money), r is the annual interest rate (in decimal), t is the time the money is invested for, and e is the base of the natural logarithm. To find the balance right before the 5th deposit, we calculate the future value of each of the previous four deposits separately and sum them up.

• First deposit: Future value after 4 years = 3500e0.08*4
• Second deposit: Future value after 3 years = 3500e0.08*3
• Third deposit: Future value after 2 years = 3500e0.08*2
• Fourth deposit: Future value after 1 year = 3500e0.08*1

The sum of these four amounts will give us the total balance right before the 5th deposit. To find the balance right after the 5th deposit, simply add the amount of the 5th deposit to the previously calculated total.