precal question

Question

A man invests $4000 in an account that pays 7.5% interest per year, compounded quarterly.

(a) Find the amount after 2 years? (Round your answer to the nearest cent.)

$ 

(b) How long will it take for the investment to double? (Round your answer to two decimal places.)

 yr

Answer 1

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

A = 4000(1 + 0.075/4)⁴⁽²⁾

A = $4640.89

8000 = 4000(1 + 0.075/4)^4t

2 = (1 + 0.075/4)^4t

log(2) = 4tlog(1 + 0.075/4)

t = log(2)/4log(1 + 0.075/4)

t = 9.33 years