When it comes to managing a savings account, it's crucial to understand how interest works and how it can be used to enhance the value of your savings over time. This article explores the calculation of compound interest in a practical scenario, providing insights into how Sajina, our hypothetical individual, can achieve specific financial goals.
Introduction to Compound Interest
Compound interest is the interest calculated on the initial principal and the accumulated interest from previous periods. Unlike simple interest, which is calculated only on the principal amount, compound interest allows your money to grow faster over time, as you earn interest on both the principal and previously earned interest.
Scenario Overview
Sajina deposited Rs 20000 into a savings account at an 8% annual interest rate. After 2 years, she withdrew Rs 5000 and the total interest earned during those 2 years. The goal now is to determine how long Sajina needs to keep her remaining balance to achieve a total interest of Rs 6800. This article delves into the detailed steps and calculations to reach the desired outcome.
Step-by-Step Calculation
Step 1: Calculate Total Interest Earned in the First 2 Years
First, we calculate the simple interest earned in the first 2 years using the formula:
SI
Where P Rs 20000, R 8%, and T 2 years.
Substituting the values:
SI
Step 2: Calculate the Total Amount After 2 Years
The total amount after 2 years is:
A P SI 20000 3200 Rs 23200
Step 3: Withdrawal After 2 Years
Sajina withdrew Rs 5000, leaving Rs 18200 in the account:
Remaining Amount 23200 - 5000 Rs 18200
Step 4: Total Interest Target
She aims for a total interest of Rs 6800. After earning Rs 3200 in the first 2 years, the additional interest needed is:
Additional Interest Needed 6800 - 3200 Rs 3600
Step 5: Calculate How Long to Keep the Remaining Amount
To find the time required to earn Rs 3600 in interest, we use the compound interest formula:
SI
where P Rs 18200, R 8%, and SI Rs 3600.
Rearranging the formula to solve for T:
T
Substituting the values:
T
Thus, Sajina needs to keep Rs 18200 for approximately 2.47 years to achieve a total interest of Rs 6800, or roughly 2 years and 6 months.
Conclusion
By understanding the mechanics of compound interest, Sajina can better manage her financial goals and achieve higher returns on her savings. The steps outlined in this article can serve as a practical guide for anyone looking to maximize the earnings from their savings accounts.