Trevon and mika have a new grandson how much money should...

Trevon and Mika have a new grandson. How much money should they invest now so that he will have $72,000 for his college education in 18 years? The money is invested at 2% compounded monthly.

Transcript

00:01 So in the question we have glenn and arlen who want to plan to invest their money for the newborn grandson so that he has $20 ,000 available for his education on his 18th birthday.

00:18 So at the age of 18 he will have $20 ,000 available and we have assumed that the growth rate is 7 % per year and it compounded semi annually so we have to find out the initial balance so which is p here we have this expression which is a plus p is equal to 20 ,000s where a is the compound interest and the p is the initial balance that some of these will be the total available balance so let's convert the rate into decimals so it will be 0 .07 and for the compound period we have 18 years and so the compound period will be each of the years will be two compound year periods so it will be 31 compound periods so as we have first year is have one compound period compounding period so let's write the formula of a which is p times one plus r to the part n plus sorry minus 1 plus p is equals to 20 ,000 so let's move that so if we solve the equation we will get the value of p so we have the values for r and n so let's take the p in common from the both here so it will be let's say one plus r to the power n minus one so yes let's solve the equation it will be r1 plus r only so we have r is equals to 0 .7 so it will be 1 plus 0 .7 to the power we have the period is 31 so it will be 31 so the value of 1 plus sorry it will be 0 .07 so the 1 plus 0 .07 to the 1 plus 0 .07 to the power 31 will be 8 point so it's in the calculation so let's put the value direct value here 20 to 20 thousand by what we have in the calculator let's say 1 .07 to the per 31 we have the value in calculator we don't need to take the approximate value so it will be 20 ,000 by the value of 1 .07 to the or 31 so the value will be 2 ,455 .46 approximately.

04:15 Yep, this is the approximate value.

04:19 So now we have the value of the initial balance which is p...

Question

Trevon and Mika have a new grandson. How much money should they invest now so that he will have $72,000 for his college education in 18 years? The money is invested at 2% compounded monthly.

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