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 with compound interest, we use the formula:
[
A = P(1 + r/n)^{nt}
]
where:
- ( A ) = future value of the investment/loan
- ( P ) = principal amount (initial deposit) = $2000
- ( r ) = annual interest rate (decimal form) = 4% = 0.04
- ( n ) = number of times interest is compounded per year (annually, so ( n = 1 ))
- ( t ) = number of years
Since the interest is compounded annually (( n = 1 )), the formula simplifies to:
[
A = P(1 + r)^t
]
After 5 Years:
[
A = 2000(1 + 0.04)^5
]
[
A = 2000(1.2167)
]
[
A \approx 2433.01
]
After 5 years, you will have approximately $2,433.01.
After 15 Years:
[
A = 2000(1 + 0.04)^{15}
]
[
A = 2000(1.8061)
]
[
A \approx 3612.17
]
After 15 years, you will have approximately $3,612.17.
Explanation:
Compound interest allows savings to grow exponentially over time because interest is earned not only on the initial deposit but also on the previously accumulated interest. This “compounding effect” makes long-term savings much more effective compared to simple interest, where interest is calculated only on the initial deposit.
In this example, the 4% annual interest rate consistently grows the balance year after year. After 5 years, the account grows by about $433, while after 15 years, it nearly doubles to $3,612.17. This demonstrates the power of long-term investing—over time, even small increases in interest rates or duration can significantly boost total savings.
By letting your money grow in an interest-bearing account and not withdrawing it, you maximize returns. This principle is fundamental in retirement planning, education savings, and general wealth accumulation.