You deposit $2000 into a savings account which is earning 4% compounded annually. How much will you have in your account after 5 years? After 15 years?
The correct answer and explanation is :
To calculate the future value of your savings account, we use the compound interest formula:
[
A = P(1 + r)^t
]
where:
- ( A ) is the future value of the investment/loan, including interest
- ( P ) is the principal amount (initial deposit) = $2000
- ( r ) is the annual interest rate (decimal form) = ( 4\% = 0.04 )
- ( t ) is the number of years
Step 1: Calculate the amount after 5 years
[
A = 2000(1 + 0.04)^5
]
[
A = 2000(1.2167)
]
[
A \approx 2433.35
]
Step 2: Calculate the amount after 15 years
[
A = 2000(1 + 0.04)^{15}
]
[
A = 2000(1.8111)
]
[
A \approx 3622.20
]
Explanation
Compound interest works by applying interest not only to the initial principal but also to the accumulated interest from previous periods. This is different from simple interest, where interest is calculated only on the initial principal.
Over 5 years, your initial $2000 grows to approximately $2433.35 due to compounding. Each year, 4% interest is added to the new balance, making the account grow faster than with simple interest.
After 15 years, the compounding effect is even more significant. Your savings grow to around $3622.20, showing the power of long-term investing with compound interest.
The key takeaway is that the longer your money stays in a compound interest account, the greater the benefits. Even a small interest rate can lead to significant growth over time. Thus, saving early and letting interest compound is a smart financial strategy.