Final answer:
Interest on savings is calculated by multiplying the principal amount by the annual interest rate and the length of the investment period, resulting in either simple or compound interest. Compound interest, which includes interest on accumulated interest, can significantly boost savings over time, analogous to compound economic growth rates.
Step-by-step explanation:
The amount of interest is determined by multiplying the amount in savings by the annual interest rate and the time period for which the money is invested. This is typically referred to as simple interest. However, with compound interest, the amount of interest earned on an investment is reinvested, so that in future periods, interest is also earned on the interest previously earned. An analogy can be drawn between this and the way GDP growth rates are calculated, as both involve an original amount, a percentage increase over time, and the amount of time over which growth occurs. Compound interest and compound growth rates, by incorporating the growth on past interest or GDP growth, lead to a significant increase over time.
To illustrate, if you deposit $100 in a savings account with a 2% annual interest rate, after one year, you will have $102. In the next year, that amount will increase to $104.04, and it will continue to grow exponentially over time because of the compound interest effect. This means that the increase in the savings is not just calculated on the original amount, but also includes the accumulated interest from previous periods, leading to a greater amount of savings in the long term. This is summarized by the rule of 70, which estimates the number of years it takes for an investment to double given a fixed annual rate of interest.