I don't quite understand what I'm doing wrong with this question. Please help.

Question

Hannah would like to make an investment that will turn 6000 dollars into 25000 dollars in 8 years. What quarterly rate of interest, compounded four times per year, must she receive to reach her goal?

 

I tried using the formula A=P(1+r/4)^nt. I wrote it as 25,000=6,000(1+r/4)^4(8), and I got rate=0.1824%, but my online homework tells me that this rate/percentage is wrong.

Answer 1

Compound interest is found by the equation:

A = P(1+r/n)^nt

A = future or final amount = 25000

P = principal investment = 6000

r = interest rate = to be determined

n = # times compounded each year = 4

t = time in years = 8

 

25000 = 6000(1+r/4)⁴⁽⁸⁾

25/6 = (1+r/4)³²

1 + r/4 = ³²√(25/6)

r/4 = ³²√(25/6) -1

r = 4[³²√(25/6) -1]

r = 0.18243

r = 18.24%

Round to however decimals you need.

 

Hope this helps.