Two Accounts Began With A Deposit Of 10,000 Each

Question

Two Accounts Each Began With A Deposit Of 10000both Accounts Have Two accounts each began with a deposit of $10,000. Both accounts have an interest rate of 6.5%, but one account compounds interest once a year while the other account compounds interest continuously. Make a table that shows the amount in each account and the interest earned after one year, five years, ten years, and twenty years. What is the amount in the account that compounds once a year after one, five, ten, and twenty years? What is the amount in the account that compounds continuously after one, five, ten, and twenty years?

Dr. Jack HW Helper · Accepted Answer

Financial institutions often employ different compounding methods to calculate interest, significantly impacting the growth of savings over time. Understanding the effects of annual and continuous compounding is essential for investors and savers to make informed decisions about their investments. This paper explores the differences between these two compounding methods by analyzing an initial deposit of $10,000 at an annual interest rate of 6.5%, comparing the accumulated amounts and interest earned over periods of one, five, ten, and twenty years. Compounding interest involves earning interest on both the initial principal and the accumulated interest from previous periods. The two primary methods examined here are annual compounding, where interest is compounded once a year, and continuous compounding, where interest is compounded at every possible instant. These methods are rooted in mathematical formulas that model the growth of an investment over time. The formula for annual compounding is given by: A = P(1 + r)^t where A is the amount in the account after time t years, P is the principal amount ($10,000), r is the annual interest rate (6.5% or 0.065), and t is the time in years. For continuous compounding, the formula is: A = P * e^{rt} where e is Euler's number (~2.71828), and other variables are as previously defined. Calculations for specific timeframes yield the following results: 1 Year Annual Compounding: $10,650.00 Continuous Compounding: $10,657.12 5 Years Annual Compounding: $13,701.55 Continuous Compounding: $13,727.34 10 Years Annual Compounding: $14,778.96 Continuous Compounding: $14,862.15 20 Years Annual Compounding: $18,255.19 Continuous Compounding: $18,371.45 These calculations show that continuous compounding results in slightly higher accumulated amounts than annual compounding over the same periods due to the more frequent accrual of interest. The differences become more pronounced over longer time horizons, emphasizing the power of contin

Two Accounts Began With A Deposit Of 10,000 Each

Two Accounts Each Began With A Deposit Of 10000both Accounts Have

Paper For Above instruction

1 Year

5 Years

10 Years

20 Years

References