Calculating Denada's Savings Total And Interest Earned After 1 Year
Hey guys! Let's dive into a super practical math problem today – calculating how much Denada's savings will grow in a year with a specific interest rate. This is something we can all relate to, whether we're saving up for a new gadget, a vacation, or just building our financial cushion. We'll break down the problem step-by-step, showing you how to calculate the total savings and the interest earned both the traditional way and using a handy formula. So, grab your calculators (or just your thinking caps!) and let's get started!
Understanding the Problem
So, Denada, our savvy saver, deposits Rp6,000,000 in a bank. The bank is offering an interest rate of 1.8% per month. That's pretty neat! The big question is: How much money will Denada have in her account after a year, and how much of that is the interest she's earned? We're going to tackle this using two methods: the simple way and the formula way. Trust me; understanding both will make you a financial whiz!
Key Terms and Concepts
Before we jump into the calculations, let's make sure we're all on the same page with some key terms:
- Principal (P): This is the initial amount of money Denada deposited, which is Rp6,000,000.
- Interest Rate (r): The percentage the bank pays on the savings. Here, it's 1.8% per month. We need to express this as a decimal for our calculations, so we divide 1.8 by 100, which gives us 0.018.
- Time (t): The duration the money is saved, in this case, 1 year. But since the interest is given monthly, we'll convert this to months, so t = 12 months.
- Interest (I): The amount of money earned on the principal due to the interest rate.
- Total Amount (A): The principal plus the interest earned (A = P + I).
Now that we're armed with these definitions, let's get calculating!
Method 1: The Step-by-Step Calculation
This method is perfect for understanding how the interest accumulates each month. It's like watching your savings grow in real-time! We'll calculate the interest earned each month and add it to the previous month's total.
Month 1
- Interest for Month 1: Principal (Rp6,000,000) * Monthly Interest Rate (0.018) = Rp108,000
- Total at the End of Month 1: Principal (Rp6,000,000) + Interest (Rp108,000) = Rp6,108,000
Month 2
- Interest for Month 2: Total from Month 1 (Rp6,108,000) * Monthly Interest Rate (0.018) = Rp109,944
- Total at the End of Month 2: Total from Month 1 (Rp6,108,000) + Interest (Rp109,944) = Rp6,217,944
We continue this process for all 12 months. I know, it sounds tedious, but it's super clear! To save us some time (and space!), let's jump to the final result. After calculating the interest and adding it to the total for each of the 12 months, we find:
- Total at the End of 1 Year: Approximately Rp7,291,449
So, after a year, Denada has around Rp7,291,449 in her account. That's a healthy growth from her initial deposit!
Calculating the Total Interest Earned
To find out how much interest Denada earned in total, we simply subtract the initial principal from the final amount:
- Total Interest Earned: Final Amount (Rp7,291,449) - Principal (Rp6,000,000) = Rp1,291,449
Wow! Denada earned a whopping Rp1,291,449 in interest. Not bad for just letting her money sit in the bank!
Method 2: Using the Compound Interest Formula
Now, for those of you who love formulas, this method is for you! It's a more direct way to calculate the total amount after a certain period, especially when we're dealing with compound interest (interest earned on both the principal and the accumulated interest).
The formula for compound interest is:
A = P (1 + r)^n
Where:
- A is the total amount after n periods (what we want to find).
- P is the principal amount (Rp6,000,000).
- r is the interest rate per period (0.018 per month).
- n is the number of periods (12 months).
Let's plug in the values:
A = 6,000,000 (1 + 0.018)^12
Step-by-Step Calculation with the Formula
- Calculate (1 + r): 1 + 0.018 = 1.018
- Calculate (1 + r)^n: 1.018^12 ≈ 1.21524122
- Multiply by the Principal: 6,000,000 * 1.21524122 ≈ 7,291,447.32
So, using the formula, we get a total amount of approximately Rp7,291,447.32. Notice that this is very close to the result we obtained using the step-by-step method. The slight difference is due to rounding in the step-by-step calculations.
Calculating the Total Interest Earned (Formula Method)
Just like before, we subtract the principal from the final amount to find the total interest earned:
- Total Interest Earned: Rp7,291,447.32 - Rp6,000,000 = Rp1,291,447.32
Again, this is very close to the interest earned calculated using the step-by-step method.
Comparing the Two Methods
Both the step-by-step method and the compound interest formula give us essentially the same result. The step-by-step method is excellent for visualizing how interest accumulates over time, while the formula provides a quicker route to the final answer, especially for longer periods. The compound interest formula is a powerful tool for financial planning and understanding the growth of investments.
Final Answers
Alright, guys, let's wrap up with the answers to our initial questions:
- Total Savings After 1 Year: Approximately Rp7,291,447 to Rp7,291,449 (depending on the method used and rounding).
- Total Interest Earned: Approximately Rp1,291,447 to Rp1,291,449.
Denada made a smart move by saving her money in a bank with a good interest rate! This example perfectly illustrates the power of compound interest and how your savings can grow over time. Remember, understanding these concepts can help you make informed financial decisions and achieve your savings goals.
Key Takeaways for Future Savers
- Start saving early: The earlier you start saving, the more time your money has to grow through compound interest.
- Understand interest rates: A higher interest rate means your money will grow faster. Shop around for the best rates!
- Be consistent: Regular savings, even small amounts, can add up significantly over time.
- Use the compound interest formula: This formula is your friend when planning for long-term financial goals.
So, there you have it! We've successfully calculated Denada's savings growth using two different methods. I hope this breakdown has been helpful and has given you a better understanding of how interest works. Now, go forth and conquer your financial goals! Happy saving, everyone!
