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The problem in the image asks for the following:

1. A loan of 1,000,000 with an interest rate of 4% per month, to be repaid over 5 months.
   Determine:
   a. The annuity (fixed monthly payment).
   b. The first month's interest.
   c. The first month's installment (principal + interest).

### Solution Steps:

Let's denote:
- \( P = 1,000,000 \) (the loan principal),
- \( i = 4\% = 0.04 \) (monthly interest rate),
- \( n = 5 \) months (the loan term).

#### a. Annuity (A)

The annuity formula for fixed monthly payments is given by:

\[
A = \frac{P \cdot i}{1 - (1 + i)^{-n}}
\]

Substituting the known values:

\[
A = \frac{1,000,000 \cdot 0.04}{1 - (1 + 0.04)^{-5}}
\]

I will calculate the annuity (monthly payment).The annuity (fixed monthly payment) is approximately \( 224,627.11 \).

#### b. First Month's Interest

The interest for the first month is calculated as:

\[
\text{First month's interest} = P \cdot i
\]

\[
\text{First month's interest} = 1,000,000 \cdot 0.04 = 40,000
\]

So, the first month's interest is \( 40,000 \).

#### c. First Month's Installment (Principal + Interest)

The first installment is the total annuity minus the interest for the first month:

\[
\text{First month's installment (principal)} = A - (\text{First month's interest})
\]

Let me calculate that next.The principal portion of the first installment is approximately \( 184,627.11 \).

### Summary:
- **a. Annuity (fixed monthly payment):** \( 224,627.11 \)
- **b. First month's interest:** \( 40,000 \)
- **c. First month's installment (principal payment):** \( 184,627.11 \)

Would you like further details or have any questions?

### Related questions:
1. How does the annuity change if the loan duration increases to 12 months?
2. What would be the total interest paid over the 5-month period?
3. How much would the second month's interest and principal portion be

Sebuah pinjaman sebesar 1.000.000 dengan bunga sebesar 4% per bulan akan dilunasi selama 5 bulan, maka tentukan: a) Anuitas, b) Bunga pertama, c) Angsuran pertama.

Learn how to calculate the annuity, interest, and first installment for a loan of 1,000,000 with a 4% monthly interest rate, to be repaid over 5 months. This example covers important concepts such as loan amortization and interest calculations.

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