00:01
Hi, from the question given that, suppose you would like to have dollar 1 ,000, triple zero, triple zero.
00:15
When you retire in 40 years.
00:18
So, this will be a future value.
00:22
And number of years, t is equal to 40 years.
00:28
And here, how much should you invest each quarter if you can earn a rate of 5 .8? 8 % so rate of interest are is equal to 5 .8 % which could be equal to 0 .058 and if the rate of interest is compounded quarterly therefore n is equal to 4.
00:52
So here in part a we need to find how much should you deposit in each quarter so here we need to find the monthly payment monthly payment pm t so if you in general formula for using future value will be equal to pm t times of 1 plus r by n the old power n t minus 1 divided by r by n so now substitute the given values so future value is 1 triple 0 which is equal to p mt is unknown value times of 1 plus r is 0 .0.
01:44
58 divided by n the old power n is here n is 4 so 4 old power 4 times of 40 minus 1 divided by 0 .058 divided by 4 so this is equal to p mt times of 1 .0145 to the power of 1 .0145 to the power of 140 60 minus 1 divided by 0 .0145.
02:26
So this is equal to pmt times of 9 .070756 divided by 0 .0145...