00:01
Hello, students, we are asked in the question that amount of money in an account growing at interest rate is given and semi -annual interest rate and formula is given.
00:12
We need to find our answers.
00:14
So let's see our principal amount is given as principal amount if i write here for this.
00:22
So basically principal amount if i write for this is thousand and in the next case what we are given interest rate is 6 % semi -annual.
00:34
So interest rate is basically 6 % semi -annual, right? semi -annual means if i write for this, let's say this is our r, right? and let's say time is t.
00:49
So r -dess would be semi -annual.
00:51
So rate would be half, right? so 3 % would be rate.
00:56
And if i write, time will be double in every case, right? so if i write here, future value would be, if i write here, amount is principal amount which is given as p, multiply by 1 plus rate value r -dash divided by 100, raise to power t -dash, right, because interest rate is semi -annual.
01:20
Right, so let's say if i put all the values, this is 1 ,000, multiply by 1 plus 3 by 100, raise to power 2t, right? and t is the value in years, t is in years, right? because interest is semi -annual.
01:40
So basically if i write for this, this is thousand multiply by one plus 0 .03 raise to power 2 t in if it is compared with this value it is same in this.
01:52
So to make it more understand we have shown this.
01:56
So in the first case what we are asked there, we are asked as find the amount of of money in the account after four years.
02:03
So t is equal to four years.
02:06
What would be the amount after this? so 80.
02:09
So we can write this as 80 what we want amount after four years.
02:15
So a four is basically thousand multiply by one plus 0 .03 raise to power eight.
02:22
4 multiply by 2.
02:23
So thousand multiply by 1 .03 raise to power 8.
02:27
So amount is if i calculate this this this will come out as 0 ,000 multiply by 0 .1266 and this is 7 .7, right? and if i calculate this, this will 1266 .77, right? this much amount and b part is, let's talk about b part, find the rate at which money is growing at year 4.
02:52
So we need to calculate the rate of changing the money amount, rate of changing of amount is calculated by d, y, by dt of that particular amount equation, right? it means we need to take d .y, y, dt of this, dy, y, dt of thousand multiplied by 1 plus 0 .03 raise to power t, right? it means we need to extract this as constant and we need to apply here.
03:23
So if i see here, raise to power t, right? here, tote will come...