Pre calculus

Question

I need help with this problem please:

 

Todd is looking to invest $5,000 in an account that pays 2.4% interest per year, compounded quarterly.   How long will it take for the money to double?

 

Thank you!!!

Answer 1

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

A = final amount = 2p

p = principal investment

r = interest rate = .024

n = #times compounded per year = 4

t = time in years = tbd

 

2p = p(1+.024/4)^4t

2 = 1.006^4t

Take log of both sides

log 2 = log 1.006^4t

log 2 = 4t(log 1.006)

 

t = (log 2)/(4 log 1.006)

 

t = 28.97 years

 

round to 29 years