# Lessons in Clarity: Quantitative Concepts

One of the biggest challenges for today’s workforce is that we are living longer, so we need to save more — and start saving sooner — to fund our retirement savings. But how do we determine how much we need to save and for how long?

In this article, we take a closer look at a key topic in the Investment Foundations course of study —  quantitative concepts (Module 3) related to the time value of money — to understand more about investing and the impact of time on your savings.

## Simple and Compound Interest

A simple interest rate is the rate of return to the lender on the original principal (the total amount borrowed). The amount of interest earned depends on the simple interest rate and the amount of principal lent or borrowed per period. This calculation is expressed as

Simple interest = Simple interest rate × Principal × Number of periods

For example, if a deposit in a bank offers a simple interest rate of 10% per year, then for every £100 deposited, the depositor will receive £10 over the course of the year:

Interest = 0.10 × £100 × 1 = £10

If the deposit is left for two years, the total interest earned will be £20:

Interest = 0.10 × £100 × 2 = £20

The underlying assumption of simple interest is that interest is not reinvested, so the interest is always calculated on the amount of the original principal.

Compound interest is the return to the lender when interest earned is added to the original principal. Compound interest is often referred to as “interest on interest.” Unlike simple interest, interest payments are assumed to be reinvested. So, interest is earned on principal and interest, not just on principal.

For example, if a deposit of £100 is made and earns 10% per year and the money remains on deposit, then interest is earned in the second year on the £10 of interest that was earned in the first year, as well as the original £100. See the following:

 Year Beginning Balance Interest Earned Interest Withdrawn Ending Balance 1 100 10 0 110 2 110 11 0 121

Note that the second year’s interest is calculated on the original £100 principal plus the first year’s interest of £10. Total interest after two years will now be £10 (= £100 × 0.10) for the first year plus £11 (= £110 × 0.10) for the second year. So, the total interest after two years is £21, rather than £20 if the interest had not been compounded.

The relationship between the original principal and its future value when interest is compounded can be generally described as

Future value = Original principal × (1 + Interest rate)Number of periods

In the deposit example, £100 × (1 + 0.10)2 = £100 × (1.10)2 = £121

The impact of compound interest can be extremely powerful, especially when the horizon is long term, such as investing for retirement. As we saw in our example, £100 invested at 10% for two years will become £121. However, the same sum invested for 20 years will become £673 with compounded interest.

That is, £100 × (1 + 0.10)20 = £100 × (1.10)20 = £673.

Whereas under simple interest, the balance at the end of 20 years would only be £300.

## Bottom Line

The impact of reinvestment (compounding) means it is critical for you to start saving money as soon as possible. Allowing the maximum length of time for your money to grow, as the example shows, lets you benefit from reinvestment and save more money to finance more years of retirement.