00:01
Hi, first we need to solve part a.
00:04
We know that the compound interest formula, a equals p into 1 plus r by n the whole power n t, where a is the final amount and p is the principal amount, r is the rate of interest and n is the number of time interest applied per period.
00:23
T is number of time periods.
00:25
Here, given that p equals $1 .25.
00:31
And the rate of interest or equals 7 % which can be written as 7 by 100 which is equal to 0 .07 we need to find the time period t a equals 60 ,000 and also n equals 1 year time period for compounded annually so we have to take n as 1 on substituting all the known values in this formula then we get a is 60 ,000 which is equal to 25 ,000 into 1 plus 0 .07 divided by 1, the whole power 1 into t, which can be simplified as 60 ,000 divided by 25 ,000 equals 1 .07 the whole power 10, the whole power t.
01:31
On dividing we get 2 .4 equals 1 .07 the whole power t.
01:38
On taking log on both sides, then we get log 2 .4 equals log 1 .07 the whole power t, which can be further simplified as log 2 .4 equals t log of 1 .07, which can be written as log 2 .4.
02:03
Divided by log 1 .07 equals t which implies t equals 12 .93.
02:15
Hence we approximated to 13 years...