BUNGA MAJEMUK DAN ANUITAS

Assalamualaikum Wr. Wb. Introduce my name, Rini Oktafeningsi. This time we will study and calculate the flower of Majemuk and annuity. For that, we continue to the first material, which is about Majemuk flowers. Majemuk flowers are flowers that will be given based on the initial capital and flower accumulation in previous periods.

Majemuk flowers also have many variations and always change in each period. Here, Ibu already has a table, which we will complete the following tables. And we will count the first flower, second flower, third flower, fourth flower, and so on.

here the flower is already 5% then the initial balance is 1 million to calculate the first flower, the second flower and the next one it is based on this

The first flower is equal to 5/100 because we change this 5% into a fraction, so it becomes 5/100 multiplied by 1 million. Here we can subtract, this is the zero, it's 2. 1, 2, we subtract, this is also 1, 2. So 5 multiplied by 10,000, how much? 50,000, put it next to this, friends.

Then, to determine the balance, we just need to add 1 million plus 50 thousand, so it becomes 1 million 50 thousand. That's for the second flower.

For the third flower, we will calculate it from the second flower. So 5/100 times 1.5 million, this is based on the last balance. So how much? We also subtract the zero from 2.

we also subtract the zero from 2, which means that there are 5 million times 10,500, the result is the flower, which means 52,500. Then to determine the balance here, it means that it is only to be multiplied.

Rp 1,050,000 plus Rp 52,500, the result is Rp 1,102,500. That means to calculate the fourth column based on the third flower, which is 5 per 100 times the last balance, how much? And so on. If possible, friends, please try to find the fourth flower.

Then, here in the jade flower, there is a formula that we must memorize and understand. Here there is Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = Mn = M

Here we go straight to the first example. Firdaus will save about 3 million in the Delwin bank with a 13% interest rate per year.

Calculate the size of the Firdaus savings after 8 years. That means we can know that what is known in the question is the M.O. M.O. is the initial capital. M.O. is 3 million. Then the I, the percentage is 13% per year. This 13% we make it into a split.

becomes 13/100 then we make it a decimal which is 0.13 because this zero has two, it means that behind the comma there are two too, friends, so don't be confused, make it a decimal which is 0.13 then the n is 8 years because here it is asked how much is the Firdaus savings after 8 years, right?

Okay, then what is asked is M8. Well, that means we use a formula to find the eighth savings, which means Mn = Mo x 1 + i ^ n. So we can immediately substitute this. Well, Mo = 3 million x 1 + 0.13 ^ 8, so this must be multiplied first, friends.

1 + 0.13 = 1.13 ^ 8 this must be calculated first we always take 3 numbers behind the comma

so that the result is appropriate. So, M8 = 3 million multiplied by 2.658 = 7.974.000 So, the total savings of Firdaus after 8 years is 7.974.000 Okay, now we enter the second question.

The Firdaus savings at this time is 14,616,000 rupiahs in the bank which gives the Majemuk flower variety 16% per year. Calculate the initial Firdaus savings if it has been saved for 6 years. If we calculated the Firdaus savings after 8 years, now we calculate the initial capital.

how much is the savings of Firdaus? let's see what we know in the question

which is M6, which is 14,616,000, then the i is 16%, then stated in decimal, which is 0,16.

Here, the n is 6 years old. The question is MO, initial savings. So when we look for MO, we use this formula. Because MO is multiplied, friends. If multiplied, it means the space is divided. So to calculate MO, it becomes MN divided by 1 plus N.

Then we can directly substitute, meaning Mn = 14,616,000 divided by 1 + 0,16 divided by n. This must be operated first, 1 + 0,16 = 1,16.

Well, this one is also operated first, ranked 6, what is the result? Remember, we always take 3 numbers behind the comma, which means 14,616,000 divided by 2.436, the result is 6 million. So, the initial savings of Firdaus is 6 million. So that's it, friends.

Then we continue to discuss annuity. What is annuity? So, annuity is a sum of the same amount of payment paid at the end of the period and consists of the flower part and the flowering part. Here, wait, here is an example of payment

A loan from a bank is the same as a loan plus a flower. We symbolize the A as an annuity, the AN as a loan, and the BN as a flower.

Where to calculate the formula for calculating the magnitude of annuity is A = m * i per 1 - 1 + i ^ - n with A = annuity, m = initial number, i = annuity flower type, n = period.

Then, to calculate the first flower's magnitude, which is BI equals M times I, then to calculate BN equals BN.

A minus AN. A is annuity, guys. Okay. Then to calculate the magnitude of AN, it means the magnitude of the question. It's possible that when you're in a question, the question is the magnitude of the eighth, tenth, twentieth, or twenty-first. So AN. The N depends on the question.

Then, AN = A1 * 1 + i ^ n - 1 So to calculate the magnitude of the equation that is asked can use a formula like this Then, AN itself when it is known the annuity and BN, can be directly reduced

Where B1 is the flower size on the first fraction, namely B1. AN is the size of the fraction to N. A1 is the size of the first fraction. With the formula to find A1 is the annuity of the flower size on the first fraction. So, like that. Now, let's go straight to the example question.

Honey buys clothes worth Rp. 5 million on Shopee using the Shopee Pay Later payment method. The annual rate is 3% per year. Honey wants to pay using the time limit of 6 times the monthly payment period.

It means that because you guys here in the question are already in accordance with the month and here also per month, right? Because the first thing you ask is how much money should be paid per month? Because it's already per month, it means you can just know that the first one is M. What is M, guys?

the initial number is 5 million then the i is equal to 3% we change it to decimal which is 0.03 so later one day this i becomes per year means you have to divide it by 12 because one year is 12 months

then the n is the same because here the n is already in the month, it means that you write the n with 6 but if the n is in the year, it means that you have to divide it by 12

Okay, then the question is how much money should be paid per month, right? Well, it means we use this formula where we can immediately substitute 5 million multiplied by 0.03 divided by 1 minus 1 plus 0.03 divided by negative n This must be operated first, then the result is like this

If there is a number like this, we operate it first. So, like this, 1,03 is divided by negative 6, which is 0,837. Remember, we always take three numbers behind the comma.

Then, this one, 1 minus 0.837, is operated first, the result is 0.163, then you can divide this one by 0.03 divided by 0.163, which is 0.184, then you can multiply it by the front one, multiplied by 5 million.

The final result is 920,000 rupiah. So the money that must be paid every period is 920,000 rupiah. Okay, this was just the A, now there is the B. The question is how many first columns of A1? How many first columns of A1? What was the formula?

The formula is A1 is equal to annuity minus B1. The annuity was already known, Rp. 920,000. Now, to find B1, we can use

this formula. Now, I remind you again, what was the i, what was the m, what was the a? The annuity was Rp. 920,000, the initial amount was Rp. 5 million, the i was 0.03. Just enter or substitute it into the formula, which is Rp. 920,000 minus Rp. 150,000. Now, where is Rp. 150,000 from? It should be from here, friends.

Here is 770, we should find B1

M divided by I is 5 million multiplied by 0.03 is 150. Now, 150 is the B1. So, 920,000 minus 150,000 is 770,000. So, A1 or the first large fraction is 770,000.

Then, how much is the 8th integer? A8. So, we can use this formula. AN is equal to A1 multiplied by 1 plus I, divided by N, minus 1. We have calculated A1, which is 770,000. So, we can immediately substitute it into the question.

770,000 multiplied by 1 plus 0.03 divided by 8 minus 1 because this formula is n minus 1, friends. Again, this is operated first. 1 plus 0.03, which is 1.03. 8 minus 1 is 7. This number must be operated first, which is 1.03.

230 because this is the mother of the circle, the mother of the circle, which after that can be multiplied by the same front, multiplied by 770,000, which is 947,100. Okay, the last one, D, how many fractions are there in the 10th or A10? Well, the formula is the same, just the difference is in the class, it means 770,000

multiplied by 1 plus 0.03 divided by 10 minus 1 we sum up, which is 1.03 then we divide by 9, which means the result is 1.305, this is already Mrs. Bulatin and Mrs. Amil took three numbers behind the comma the result is 1.004.850

So, that's it, friends. After this, there will be a question practice. There will be four questions. Please work on it with good and correct following the rules and explanations that I have explained. Good luck!

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