BUNGA TUNGGAL APLIKASI DERET ARITMATIKA MATEMATIKA WAJIB KELAS XI KURIKULUM MERDEKA VIDEO 1

Assalamualaikum warahmatullahi wabarakatuh. Welcome back to the Teladan Mathematics channel. This time we will discuss the subject of Mathematics compulsory class 11 about flowers and annuity.

We start with the flower matter first. Here is a definition of a flower, where a flower is a service for the use of a number of money or capital paid at the agreed time. Generally, flowers are stated in percentage form. Then,

We need to know that the period of counting flowers on the amount of capital that is stored in the bank is not the same. There are those that last one day, there are those that last one month, there are those that last one year, and so on. Okay, here are two types of flowers. The first type we will discuss is the single flower. The definition is

The value of a flower, whether taken or not taken, does not get a flower in the calculation of the next flower period, called a single flower. Okay, if we have a capital of M0, the initial capital, let's say, that we keep in the bank, with a single flower of I in one period, then

After the first period, the money that was saved earlier will become, let's say, M1. After one period, it becomes M1, equal to the initial capital plus the multiplication between the amount of flowers multiplied by the initial capital. So I repeat again, after one period, our money becomes the initial capital plus the amount of flowers multiplied by the initial capital. Now, if we factor this into M0,

multiplied by 1 plus i, where i is the flower's value. Then after the second prediction, the modality will be the expression of m2. m2 equals m1 plus flower multiplied by m0, still multiplied by m0, not m1. These are the characteristics of a single flower. So m2 equals m1, plus the single flower's value multiplied by

the initial model or the original model. We know that m1 is m0 times 1 plus i. We can change it to m0 times 1 plus i plus i times m0. If we subtract this, m0 times 1, m0 times i, then we get m0 times 1 plus i plus i. Sorry, we factor this.

So we get M0, so M0 times 1 plus i plus i. This can be multiplied by i with i. So we have M0 times 1 plus 2i. So after the second period, the money that is saved or the model that is saved becomes M0 times 1 plus 2i. Then in the same way, after the third period, the model will become M3, the same as M2 plus

single flower multiplied by m0. We have m2, we immediately substitute m2, plus i times m0. If we remove m0, then we have the formula m0 multiplied by 1 plus 2i plus i. 2i plus i will be 3i, so we have the final result m3 is equal to m0 multiplied by 1 plus 3i.

And then, in the same way, after the period of n later, let's say until the period of n, the capital will be Mn = M0 + n*i. We pay attention here. M2, 2i, M3, 3i, then Mn must be n, ni. So in the period of n, the capital becomes M0 * 1 + ni.

Okay, we will discuss some examples of the following questions related to capital after the NDP period. Okay, the first example. The amount of 10 million is stored in the bank with a single interest rate of 1% per month. If the amount is stored for 10 months, then the amount will be. Okay, we will answer it right away. But first we write the information given in the question.

It is known that the first is M0, the initial capital is 10 million, then N is 10, because the period is a month. Here for 10 months, so N is 10 and the single flower is 1% per month. So 1/100 = 0.01 and the question is MN, where N is 10, so the question is M10.

Okay, let's just write the formula first. Mn is m0, initial capital multiplied by 1 plus ni. Because n is 10, then it becomes m10, m0 is 10 million multiplied by 1 plus n, n is 10 multiplied by i, i is 1%, or 0.01.

So M0 = 10 million multiplied by 1 plus 10 multiplied by 0.01. 10 multiplied by 0.01 is 0.1. So 10 million multiplied by 1 plus 0.1. Then the next step is to try to sum 1 with 0.1, then we get 1.1.

So we just multiply to get M10, 10 million multiplied by 1.1 equals 11 million. So the conclusion is after 10 months the capital becomes 11 million rupiah. Okay, let's continue to the second example. Debt of 2.5 million rupiahs, single-use, equals 12% per year.

Remember per year, yes, earlier per month, now we are per year. If the debt is returned for 5 months, returned after 5 months, then the amount that must be paid is, okay, as usual we write the information given in the question, the first is the initial debt of 2.5 million, yes, N is 5 in a month, then the annual interest rate is 20% per year.

We make it 12% per 12 months, because 1 year is 12 months. So 12% divided by 12 is equal to 1% per month. Make it decimal, so it becomes 0.01. Meanwhile, the question is the value of mn, where n is 5, so m5.

With the same formula, we use the formula = m0 * 1 + ni = m0 = 2.5 million * 1 + n * i = 1% = 0.01

So 5 times 0.01 is 0.05 plus 1 becomes 1.05. Now we just multiply 1.05 by 2.500.000. Then we get what has to be paid is 2.625.000 rupiah. This is the money that has to be returned after 5 months. Okay, next in the following example,

A trader saves money in the bank as much as X rupiah with a single 2% per month. If yes, after one year the money becomes 310,000 rupiah, then what is the value of X, or how much money was saved at the beginning? As usual, we write what is informed. We need to know that one year is equal to 12 months. What we know is the M12.

So after 12 months, the stored amount is 310,000. The n is 12 per unit. Then the single flower density is 2% per month. So 2 per 100 equals 0.02. The question is how much is m0 or x? With the same number, mn equals m0 multiplied by 1 times mi. Then if we pay attention, now we already have mn, 310,000.

We still have Mn, M0 is the X that is asked, N we have 12, we have 2% of I. If we substitute M12 is 310,000, the initial capital X multiplied by 1 plus 12 times 0.02, 2%. 12 times 0.02 is 0.24.

plus 1, so we have 1.24. So 310,000 is equal to x times 1.24. To get the value of x, then we divide the two squares by 1.24. So x is equal to 310,000 divided by 1.24. Then we get the value of x is 250,000 rupiah.

So the conclusion is the initial capital saved is 250,000 rupiah. Well, this is the first video about the single flower tribe. Wait for the continuation video, of course, on the same channel, the Matematika Teladan channel. Hopefully useful. Wassalamualaikum warahmatullahi wabarakatuh.