00:01
So for part a here, we have a interest rate of 4 .5 % compounded quarterly.
00:12
So r over n is 0 .045 over 4 is 0 .0125.
00:25
Nope.
00:30
1, 0 .01125 per quarter.
00:41
And we want to do this for 30 months, which is 30 quarters.
00:56
And we want to know the present value in order to have a future value of 10 ,000.
01:10
So this then is equal to the future value times 1 plus r over n to the negative t, where t is the number of quarters, because rn is your interest rate per quarter.
01:33
So our present value then is 10 ,000 times 1 .01125 to the negative 30 quarters.
01:47
And that is equal to 10 ,000 times 1 plus 0 .045 divided by 4 to the negative 30.
02:21
7, the $148 .98.
02:27
So this is what you would have to deposit today.
02:30
And now for part b, our present value is 20 ,000.
02:37
We want to earn interest that totals 1 ,000 in three years.
02:48
And this means that our future value is the present value plus the interest of 21 ,000.
02:57
And we want to know what annual interest rate would we have to earn, assuming it is compounded monthly.
03:11
So n is 12...