# Compounding quarterly!

• Apr 22nd 2008, 11:15 AM
evinez
Compounding quarterly!
find the time required for an investment of 5000 dollars to grow to 9000 dollars at an interest rate of 7.5 percent per year, compounded quarterly.

t= _____

this is what i have got so far please correct me if i am wrong

9000=5000(1+.075/4)^4t

so you divide by 5000 on each side leaving you with
9000/5000= 1.8

1.8= (1+.075/4)^4t

Ln1.8 = Ln(1+.075/4)^4t

divide by 4(1+.075/4)

ln1.8/4ln(1+.075/4) = t

then whats next? cuz i got that this above part equals 7.9

so then i replugged it back into the first equation but it says its not correct

8993.04676

used 7.9 ??
• Apr 22nd 2008, 11:31 AM
earboth
Quote:

Originally Posted by evinez
find the time required for an investment of 5000 dollars to grow to 9000 dollars at an interest rate of 7.5 percent per year, compounded quarterly.

t= _____

this is what i have got so far please correct me if i am wrong

9000=5000(1+.075/4)^4t

so you divide by 5000 on each side leaving you with
9000/5000= 1.8

1.8= (1+.075/4)^4t

Ln1.8 = Ln(1+.075/4)^4t

divide by 4(1+.075/4)

$\ln1.8/{\color{red}(} 4\ln(1+.075/4)/{\color{red})} = t$

then whats next? cuz i got that this above part equals -.584

If you use brackets then you'll get $t =7.9$