Question

part 3: the power of compounding
use the compound interest calculator (qr code) to answer the questions for each of the following scenarios.
here are a few things to do when using the calculator:

• the initial investment will be the same as the monthly contribution.
• set the compound frequency to annually.
• round all monetary answers to the nearest whole dollar.

scenario #1: raul
raul is a saver. he sets aside $100 per month during his career of 40 years to prepare for retirement. he does not like the idea of investing because he prefers to minimize his risk as much as possible, so he puts his money in a savings account which earns 1.5% interest per year.

1. what is the total balance in the account after 40 years? $65,302.87
2. how much of the total did raul contribute himself? $48,100.00
3. how much money did raul make through compound interest in this savings account? $17,202.87
4. identify one way raul could have increased the total amount of money he made over the 40 years. explain your reasoning.

scenario #2: pamela
pamela is also a saver. she sets aside $100 per month during her 40 year career. she invests in the us stock market* through an index fund that averages a 7% annual return over this 40 year period.

1. what is the total balance in the account after 40 years? $241,059.58
2. how much of the total did pamela contribute herself? $43,300.00
3. how much money did pamela make through compounded returns in this investment account? $197,759.58
4. why is pamela’s total balance so much greater than raul’s even though she contributed the same amount as he did?

*note: we use 7% as the annual return of the stock market (based on historical averages) for simplicity. however, keep in mind that, unlike a savings account, the stock market does not guarantee any specific return rate. stocks rise and fall in price daily, and even throughout the day, so your total earnings ultimately depend on the price at which you buy and sell the shares.

Explanation:

Step1: Answer Q4 (Raul's growth method)

Raul could increase his monthly contribution. If he saves more each month, the principal for compounding grows larger, leading to more total interest over 40 years. For example, if he saves $150/month instead of $100, the total contributions become $150*12*40 = $72,000, and the compound interest on this larger principal will result in a far higher final balance.

Step2: Answer Q8 (Pamela vs Raul difference)

The core difference is the annual interest/return rate. Raul's savings account only earns 1.5% annual interest, while Pamela's index fund averages 7% annual returns. Compound interest grows exponentially with higher rates, so over 40 years, the much higher return rate leads to a drastically larger total balance, even with the same monthly contribution.

Answer:

1. One way: Increase his monthly contribution. A higher monthly deposit means a larger principal base for compound interest, which will grow to a much larger total over 40 years.
2. Pamela's total balance is far larger because her investment has a much higher annual return rate (7% vs. Raul's 1.5%). Compound returns grow exponentially, so the higher rate leads to massive growth of her investment over the 40-year period, even with the same monthly contribution as Raul.