Which savings account will earn you the least money?
a.One that compounds interest daily.
b.One that earns simple interest daily.
c.One that compounds interest monthly.
d.One that earns simple interest monthly.
The Correct Answer and Explanation is :
The savings account that will earn you the least money is d. One that earns simple interest monthly.
Explanation:
To understand why a savings account that earns simple interest monthly will yield the least amount of money, it’s essential to compare the different types of interest: simple interest and compound interest.
- Simple Interest: This is calculated only on the principal amount, which is the initial sum of money deposited. The formula for simple interest is:
[
\text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time}
]
In the case of a monthly simple interest account, the interest is calculated at the end of each month and is based solely on the original principal, regardless of how long the money is in the account. - Compound Interest: In contrast, compound interest is calculated on both the principal and the accumulated interest from previous periods. The more frequently interest is compounded, the more interest you earn on your total balance. The formula for compound interest is:
[
A = P \left(1 + \frac{r}{n}\right)^{nt}
]
where (A) is the amount of money accumulated after n years, including interest, (P) is the principal amount, (r) is the annual interest rate, and (n) is the number of times that interest is compounded per year.
When comparing the options:
- Daily compounding (Option a) will yield the highest return because it calculates interest daily, allowing for more frequent accumulation of interest.
- Daily simple interest (Option b) earns less than daily compounding but more than monthly simple interest because it still accrues interest daily.
- Monthly compounding (Option c) earns more than monthly simple interest because it compounds the interest earned each month.
Thus, the account that earns simple interest monthly (Option d) will earn the least money overall since it only pays interest on the initial principal each month without the benefit of compounding.