Math Problem Statement

Sistem bunga tunggal umumnya digunakan pada deposito. Tabel berikut mencatatkan uang yang didaposito berdasarkan beberapa bank. Perhitungan bunga dilakukan tiap akhir tahun. Lengkapilah tabel berikut.

Solution

The question presented in the image is about calculating the final amount of money using the simple interest formula, applied to three different initial amounts deposited in different banks, with varying interest rates and time periods.

Let's break it down step by step.

Simple Interest Formula:

A=P+(P×r×t)A = P + (P \times r \times t) Where:

  • AA = Final amount (modal akhir)
  • PP = Principal amount (modal awal)
  • rr = Annual interest rate (suku bunga per tahun)
  • tt = Time period in years (jangka waktu)

Now, let’s calculate for each scenario based on the provided data.

1. First case:

  • Principal (P) = 30,000,000
  • Rate (r) = 3% per year = 0.03
  • Time (t) = 6 years
  • Final amount (A) = 30,000,000 (already given)

2. Second case:

  • Principal (P) = 25,000,000
  • Rate (r) = 2.5% per year = 0.025
  • Time (t) = 5 years

Let's calculate the final amount:

A=25,000,000+(25,000,000×0.025×5)A = 25,000,000 + (25,000,000 \times 0.025 \times 5)

3. Third case:

  • Principal (P) = 40,000,000
  • Rate (r) = 2% per year = 0.02
  • Time (t) = 10 years
  • Final amount (A) = 21,000,000 (already given)

I will now calculate the second case using the formula.For the second case:

  • The final amount is 28,125,000 Rupiah.

Now the table looks as follows:

Modal Awal (P)Suku BungaJangka WaktuModal Akhir (A)
30,000,0003%/tahun6 tahun30,000,000
25,000,0002.5%/tahun5 tahun28,125,000
40,000,0002%/tahun10 tahun21,000,000

Would you like further clarification, or have any other questions?

Here are five related questions to expand the topic:

  1. How would compound interest affect the final amounts in these cases?
  2. What is the difference between simple and compound interest formulas?
  3. How does changing the interest rate impact the total interest earned over time?
  4. Can you calculate the interest amount earned separately from the final amount?
  5. What happens if the time period is halved or doubled in these cases?

Tip: Always check if the interest is simple or compound when calculating investments, as compound interest grows faster over time.

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Math Problem Analysis

Mathematical Concepts

Simple Interest
Percentage
Linear Growth

Formulas

A = P + (P × r × t)

Theorems

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Suitable Grade Level

Grades 9-11