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Chapter 5: Problem 45

Explain why simple interest is not the appropriate way to measure interest on a savings account that pays interest directly into your account.

Short Answer

Expert verified
Simple interest is not appropriate for measuring interest on a savings account that pays interest directly into the account because it doesn't account for the compounding effect. The main limitation of simple interest is that it computes interest on the initial principal amount only and doesn't consider interest earned on previous interest amounts. Conversely, compound interest accurately measures the growth of a savings account by considering interest earned on both the original principal and any interest that has already been paid. This results in a progressively larger principal amount over time and a higher total amount of interest earned, making compound interest more suitable for savings accounts meant for long-term savings.

Step by step solution

01

Define Simple Interest

Simple interest is a way to calculate the interest earned on an initial principal amount. The interest earned does not change over time and is calculated as a fixed percentage of the principal amount. The formula for simple interest is: \(I = P 脳 r 脳 t\), where \(I\) is the interest earned, \(P\) is the principal amount, \(r\) is the interest rate and \(t\) is the time (usually in years) the money is invested for.
02

Explain the Limitations of Simple Interest

The main limitation of simple interest is that it does not consider the interest earned on previous interest amounts. In other words, it does not take into account the effect of compounding. In the case of a savings account that pays interest directly into the account, the interest earned is automatically added to the principal, increasing the balance of the account. Simple interest does not account for this increase in principal, and therefore is not an accurate way to measure the growth of the account.
03

Define Compound Interest

Compound interest is a way to calculate the interest earned on an initial principal amount, as well as the interest earned on any previous interest amounts. This means that interest is earned on both the original principal and any interest that has already been paid. The formula for compound interest is: \(A = P 脳 (1 + r/n)^{(n 脳 t)}\), where \(A\) is the final amount, \(P\) is the principal amount, \(r\) is the interest rate, \(n\) is the number of times interest is compounded per year, and \(t\) is the time (usually in years) the money is invested for.
04

Explain the advantages of using compound interest to measure interest on a savings account

Using compound interest provides a more accurate representation of the growth of a savings account that pays interest directly into the account. This is because compound interest accounts for the changes in principal due to the addition of interest earned. Over time, the effect of compounding can result in much higher amounts of interest earned compared to simple interest, as the interest is earned on a progressively larger principal amount. This is especially relevant to savings accounts, as they are typically meant for long-term savings and can benefit significantly from the compounding effect.

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