Determine the amount of money, to the nearest dollar, you must invest at 6.2% per year, compounded semi-annually, so that you will be a millionaire in 24 years.

Question

anonymous · Answer

@ranga

ranga · Answer

The compound interest formula: $$\Large A = P(1 + \frac{ r }{ n })^{nt}$$A = Amount at maturity = $1,000,000
P = Principal Amount
r = Annual interest rate in decimal = 0.062
n = compounding period (compounded how many times a year) = 2
t = years invested = 24

Plug in the numbers and solve for P.

anonymous · Answer

hmm for some reason it is wrong

anonymous · Answer

i know the answer is $230,985.15 i just don't know how they got it

anonymous · Answer

@ranga

ranga · Answer

1,000,000 = P(1 + 0.062/2)^(2*24)
                 = P(1.031)^48
P = 1000000 / (1.031)^48 = ?

anonymous · Answer

ohhhhhhh i was putting everything on the calculator you need to solve separately correct? @ranga

ranga · Answer

You can enter everything in the calculator all at once if you make proper use of parenthesis.

anonymous · Answer

oh thats where i messed up thank you i was wondering what i was doing wrong

ranga · Answer

You are welcome.  I am getting $230,985.15

anonymous · Answer

yes same here! so instead of multiplying 1000000*1.031up48 you divide as 1000000/1.031up48 @ranga

ranga · Answer

Yes because in this problem they give you A and ask for P.  Usually in compound interest calculations they give P and ask for A.

anonymous · Answer

oh ok i understand now thank you!