Math Problem Statement

The image contains five financial math questions related to interest and annuities.

Solution

The image contains five financial math questions related to interest and annuities in Indonesian. Let me transcribe and explain them:


Soal Ulangan Harian: Bunga dan Anuitas

  1. Bu Yani menyimpan uang di bank A sebesar Rp 20.000.000,- dengan menggunakan sistem bunga tunggal per tahun. Jika selama 6 bulan uang Bu Yani menjadi Rp 21.200.000,-. Maka persentase yang diberikan oleh bank A adalah ....

    Translation: Mrs. Yani deposits Rp 20,000,000 in Bank A using a simple interest system per year. If after 6 months, her money becomes Rp 21,200,000, what is the percentage given by the bank?


  1. Pada tahun 2011, Eka menabung uang Rp 10.000.000,- dengan bunga majemuk. Jika pada tahun 2020 tabungan Eka menjadi Rp 80.000.000,- , maka tabungan Eka pada tahun 2017 adalah ....

    Translation: In 2011, Eka saved Rp 10,000,000 with compound interest. If by 2020 her savings became Rp 80,000,000, how much were her savings in 2017?


  1. Imam dan Rian menabung dengan bunga majemuk. Setelah 12 tahun, uang yang dimiliki Imam Rp 8.000.000,- lebih banyak daripada uang Rian. Jika pada tahun ke-24 selisih uang Imam dan Rian menjadi Rp 14.000.000,-, maka selisih uang Imam dan Rian pada awalnya adalah ...

    Translation: Imam and Rian save money with compound interest. After 12 years, Imam's money is Rp 8,000,000 more than Rian's. If after 24 years, the difference between Imam's and Rian's money becomes Rp 14,000,000, what was the initial difference?


  1. Suatu pinjaman dengan suku bunga majemuk 13% per tahun akan dilunasi dengan anuitas tahunan. Jika angsuran kedua dari pinjaman tersebut adalah Rp 734.500,-. Maka besar angsuran ke 4 adalah ....

    Translation: A loan with a compound interest rate of 13% per year will be paid off with annual annuities. If the second installment is Rp 734,500, what is the amount of the 4th installment?


  1. Seorang pedagang meminjam uang di bank sebesar Rp 10.000.000,- yang akan dilunasi selama setahun menggunakan anuitas bulanan. Jika besar bunga pinjaman 6% per tahun, maka tentukan:

    a. Besar anuitasnya

    b. Besar angsuran ke 5

    c. Sisa hutang pada akhir bulan ke 7

    Translation: A trader borrows Rp 10,000,000 from a bank, to be paid off in one year using monthly annuities. If the interest rate is 6% per year, determine:

    a. The amount of the annuity

    b. The amount of the 5th installment

    c. The remaining debt at the end of the 7th month


Would you like a detailed solution for any of these problems?

Here are 5 related questions for practice:

  1. How do you calculate simple interest for different periods of time?
  2. What is the formula for compound interest, and how does it differ from simple interest?
  3. How do you calculate the amount of an annuity for a loan?
  4. What are the differences between monthly and annual annuities?
  5. How does compound interest affect savings over different time periods?

Tip: When solving compound interest problems, ensure that you pay attention to whether the interest is compounded annually, monthly, or at another interval, as this can change the final result significantly.

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Math Problem Analysis

Mathematical Concepts

Simple Interest
Compound Interest
Annuities
Loan Repayment

Formulas

Simple Interest Formula: A = P(1 + rt)
Compound Interest Formula: A = P(1 + r/n)^(nt)
Annuity Payment Formula: P = (A * r) / (1 - (1 + r)^-n)

Theorems

Time Value of Money
Compound Interest Theorem

Suitable Grade Level

Grades 10-12