00:01
Okay, in this question we have to find out how long will it take? it means we have to find out the time period.
00:05
How long will it take an investment of $6 ,000, that is p is given $6 ,000 to grow to $7 ,000.
00:15
So accumulated value is given also $7 ,000.
00:17
If the investment earned interest at the rate of 7 .5 % per year, so r is given 7 .5 % per year.
00:26
So it is in percent, we can say it will be 0 .0 .0.
00:30
075 and we have to find out we will if the interest compounded continuously okay so if the interest compounded continuously we have to find out the time period so no problem if the interest compounded continuously the formula of accumulated value is a equals to p e raised to the power r t and now we will put all the values that we have so a is 7000 p is 6 ,000 and e raised to the power r t r is we have 0 .075 and t is we have 0 .075 and t is we have so now we have to find out the value of t no problem first of all we will make it simple and we will divide both side of the equation by 6 ,000 so it will be 7 ,000 divided by 6 ,000 equals to e -raised to the power 0 .075 t and now we can say it will be e -raised to the power 0 .075 t equals to 7 ,000 by 6 ,000 we can simply say 7 by 6 okay, and now we have to find out the value of t that is in the exponent so we will take natural logarithm in the both side of the equation and it will be ln e raised to the power 0 .075 t equals to ln 7 by 6.
01:35
No problem.
01:36
And now we know the property of logarithm that is lna raised to the power b, it will be lna...