Issue A: For The Last 19 Years, Mary Has Been Depositing

Issue A for The Last 19 Years Mary Has Been Deposi

For the last 19 years, Mary has been depositing $500 annually into her savings account, which earns 5% interest compounded annually. She plans to make one more deposit of $500 one year from today. After that deposit, she intends to close the account. The question is: how much will the account be worth at that time?

Using the future value of an ordinary annuity formula, the account’s value after 19 deposits can be calculated. The future value of an annuity compound per period is typically found using the formula: FV = A × (FVIFA i%, n), where A is the annual deposit, i% is the interest rate, and n is the number of periods.

In this case, A = $500, i = 5%, and n = 20 (including the final deposit). From Appendix C, FVIFA (5%, 20 periods) is approximately 26.3669. Therefore, the future value after 20 years—the point immediately after the last deposit—is:

FV = $500 × 26.3669 ≈ $13,183.45

Thus, at the point Mary makes her final deposit and closes the account, the account will be worth approximately $13,183.45.

Paper For Above instruction

Mary's long-term savings strategy demonstrates the power of compound interest over nearly two decades. The scenario involves a consistent annual deposit of $500 into an interest-bearing account at a 5% annual rate, compounded annually. To determine how much the account will be worth upon its closure after the last deposit, it is essential to understand the concept of future value of an ordinary annuity.

The future value of an ordinary annuity accounts for the accumulated value of regular payments over multiple periods, considering compound interest. The formula FV = A × (FVIFA i%, n), where FVIFA is the future value interest factor for an ordinary annuity, simplifies the calculation. Consulting financial tables or appendix data, FVIFA (5%, 20 periods) is approximately 26.3669, indicating the growth multiplier for such payments over 20 years.

Calculating the total value, the last deposit of $500, when compounded at 5% for 20 periods, accumulates to approximately $13,183.45. This total reflects the value of all deposits made over the 19-year period, plus the final deposit, just before Mary withdraws the funds.

This scenario illustrates the importance of consistent saving and the benefits of compound interest. As the deposit amount, interest rate, and time horizon influence the final account balance, consumers and investors can use similar calculations to plan for retirement or large future expenses. Understanding the future value of a series of payments enables better financial decision-making and effective savings planning.

Additionally, the calculation underscores the crucial role interest rates play in savings growth. Small differences in interest rates can substantially change the accumulated amount, emphasizing the importance of choosing accounts with higher returns where appropriate, and making regular contributions over time.

References

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