The following formula is applicable;
A=P(1+r)^n
Where,
A = Total amount accrued after 10 years (this is the amount from which the yearly withdrawals will be made from for the 30 years after retirement)
P=Amount invested today
r= Annual compound interest for the 10 years before retirement
n= Number of years the investments will be made.
Therefore,
A= Yearly withdrawals*30 years = $25,000*30 = $750,000
r= 9% = 0.09
n= 10 years
P= A/{(1+r)^n} = 750,000/{(1+0.09)^10} = $316,808.11
Therefore, he should invest $316,808.11 today.
To find t? yes.
First, you combine like terms so 3t and 2t and 4t. Add 3 and 2 and then subtract the 4. you will end up with 1t (just t) +2. you cannot add the 2 because it does not have the variable t. on the other side, you will also combine like terms. so 3+5=8. now your equation is t+2=8. this is the part where you will try to get t by itself. subtract the 2 from the left side. but in order for the equation to stay equal to itself, you have to subtract 2 from the right side as well. this will leave you with your final answer of t=6.
Well, your equation y=3/SQRT(3x+4) should be rationalized, but that's not what you want.
If f(x) = 3/SQRT(x+4) and g(x) = 3x
f(g(x)) then = 3/SQRT(3x+4), but rationalizing this = 3SQRT(3x+4)/(3x+4)
