00:01
In this problem, it is said that a woman who is 48 years old is employed by a firm which guarantees her a pension of $45 ,000 per year at $8 .65.
00:10
We need to find the present value of her first year's pension of the inflation over the next 17 years is 4 % per year compounded continuously, 6 % per year compounded continuously, 10 % per year compounded continuously.
00:24
So consider the formula for when we continuously compound, the final amount will be the present value times, e to the power of rt, where r is the rate and t is the time in years.
00:36
So we want to find the present value, so that's just going to be a divided by e to the power of rt.
00:42
So if we consider our first case, then the present value will be the amount, which is 45 ,000 divided by e to the power of rt.
00:51
What is r? we're considering 4 % per year for inflation.
00:56
So r is 4%, which is 4 over 100 or 0 .04.
00:59
And the time t is 17 because we're considering 17 years.
01:03
This is approximately 22797 .76.
01:09
So this will be a required answer...