00:01
Hi, in this problem, we are required to find the principal amount or the initial amount deposited with the final amount in the third year, which is equivalent to third year of the money amount is 4 ,499 .0.
00:20
It doesn't have a unit, but let's just say this is in dollars.
00:26
And on the first year, the rate is only 3%.
00:30
In the second year, the rate is added 1%.
00:33
It became 4%.
00:35
And in the third year, its rate is now 5%.
00:43
Now, what do we need to solve? we need to find for the principal amount, or we'll say, p1.
00:49
So how do we solve this? we know that finding the final amount, we just have to use this formula, where p is the a is the final amount.
01:01
P is the principal and we'll multiply it by 1 plus the number, i mean the interest rate, let's say r over, the number of times it is compounded, raise to the power of n again, and then see the time of period that has laps.
01:25
So let's start.
01:28
So take note that every year they have different rates.
01:32
So first, for the first year where the interest is only 3%.
01:39
So let's write the final amount of the first year is equal to p1 multiplied by 1 plus r1, which is 0 .03 later i will substitute it.
02:00
This is just to the power of n to the t.
02:04
So our n and t is just also equal to the t.
02:07
Because it is only compounded once every year.
02:11
So let's substitute.
02:12
We don't have the value of b1.
02:14
This is our unknown.
02:15
One plus the rate, which is, okay, let's write the rate later.
02:23
Let's just cancel out the one.
02:26
And then this one is just one multiplied by one.
02:31
This one.
02:33
So we have value of a1, which is 122.
02:41
P1 plus r1.
02:45
Now, for the second year, we use the same formula, but in this case, our principal amount is the final amount of the preceding year, that is a1.
02:59
A1, so a1 is equal to p2.
03:05
I'm sorry, this isn't for the third year, this is for the second year.
03:11
Second year, a1, same number of n and c, so it's just 1 plus r2, or the rate later, i will substitute the values, which is 3, 4, and 5%.
03:31
Now we have the value of a2...