Question

Sue plans to save $100 per month for the next 30 years to have a nest egg for retirement. Her sister, Lynn, has decided to wait and start saving $200 per month for half the time figuring she will do at least as well as her sister with this strategy. Explain why this is or is not a good strategy. You will need to make up an APR for illustrative purposes.

a) Sue's strategy is better because of the longer saving period.
b) Lynn's strategy is better because of the higher monthly savings amount.
c) Both strategies are equally effective.
d) Neither strategy is optimal due to lack of information.

Answer 1

To determine whether Sue's or Lynn's retirement saving strategy is better, a 7% APR compounded monthly is assumed. Sue's longer investment period combined with the effects of compound interest likely provides a greater future value, despite Lynn's higher monthly savings amount.

Step-by-step explanation:

When it comes to saving for retirement, both the amount saved each month and the length of time that money is saved and invested are important. To illustrate which strategy might be better between Sue and Lynn's approaches, we can use an example Annual Percentage Rate (APR) for compound interest. Let's assume an APR of 7%, compounded monthly, for simplicity.

First, let's calculate Sue's strategy. She saves $100 per month for 30 years. The formula for the future value of an annuity (series of regular savings) can be expressed as:

FV = P × { [(1 + r)^n - 1] / r }
FV: future value
P: monthly savings
r: monthly interest rate (APR/12)
n: total number of deposits (years × 12)

So, FV = $100 × { [(1 + 0.07/12)^(30×12) - 1] / (0.07/12) } |
After calculating, we'll find the future value for Sue's investment.

Now, for Lynn's strategy, who saves $200 per month for 15 years:
FV = $200 × {[(1 + 0.07/12)^(15×12) - 1] / (0.07/12)} |
Again, calculating this will give us the future value for Lynn's investment.

Comparing these two sums will help us see which strategy ultimately results in a larger nest egg. Due to the nature of compound interest, starting earlier often leads to a larger end amount, as the interest has more time to compound. Therefore, even though Lynn is saving more per month, Sue's longer investment period likely gives her an advantage, especially considering the exponential growth afforded by compound interest over longer periods.