Question

Overview

Mary has been working for a university for almost 25 years and is now approaching retirement. She wants to address several financial issues before her retirement and has asked you to help her resolve the situations below.

Issue A:

For the last 19 years, Mary has been depositing $500 in her savings account , which has earned 5% per year, compounded annually and is expected to continue paying that amount. Mary will make one more $500 deposit one year from today. If Mary closes the account right after she makes the last deposit, how much will this account be worth at that time?

Instructions

Create a spreadsheet or other document, calculating parts A of the assignment, and provide a brief explanation for each component including its significance.

Answer 1

Mary deposited $5,00 for 20 years ( 19 years + one year from now - which is last deposit ) @5% interest compounded annually. And she makes one more $5,00 deposit for one year from now.

​​​​​​A. Initial deposit of $5,00 for 20 years:

We need to find the Future value of Annuity,

Formula for future value of Annuity is, = P* ( (1+r)ⁿ - 1)/r

Where P = annual deposit amount,

r = interest rate

n = number of years

In the given case, P= $5,00 , r= 5%, n = 20

If we substitute,

Future value of Annuity= 500* ((1+0.05)²⁰-1)/0.05

On solving Future Value of Annuity= $16,530

B. One more $5,00 deposit is made for one more year from today.

Therefore the Future value of $5,00 for one year is = Present value*(1+r)ⁿ

= 500*(1+r)¹ = 500*(1+0.05) = $525

The worth of her savings account on that date would be sum of A and B, that is 16,530+525 = $17,055