00:01
So in the given question we are told that suppose that 25 ,000 from a retirement account is invested in a large cap stock fund and after 20 years the value is 156 ,000 and 372.
00:19
So what we have is we are told that the principal amount or the initial amount is 25 ,000 which is invested.
00:30
In a large cap stock fund large cap stock fund and after 20 years after 20 years we are told that the accumulated amount is 156 ,000 three hundred and seventy -two point eight dollars now what we are asked is how long will it take the investment to reach one quarter million dollars and this is what we need to find how many years would it take right so we are given this this data and we are told to use a formula called a is equal to p times e to the power r times t and first what we were told to find is the average rate of return which is given as which is given as r and r is found to be 9 .2 percentage.
01:38
So if r is found to be 9 .2 percentage for the accumulated amount to be a quarter of a million dollars which is $250 ,000, what should be the time is what we need to find? the principal amount is the same, that is $25 ,000.
02:03
So at a rate that we have calculated, that is 9 .2 percentage.
02:09
If we take the formula, it would be 250 ,000 is equal to 25 ,000 times e to the power 9 .2 percentage, that is 0 .092 times t.
02:25
And from this we can write 250 ,000 divided by 25 ,000 is 10, 10 is equal to e to the power of 0 .092 times t...