Investment Growth

Question

Find the time required for an investment of 5000 dollars to grow to 8000 dollars at an interest rate of 7.5 percent per year, compounded quarterly.

Answer 1

general formula is: A=P(1+r/n)^nt

where P = investment = 5000

A = ending Amount = 8000

r = interest rate = APR = 7.5% = .075

n = number of compounding periods per year = 4 for quarterly compoounding

8000 = 5000(1+ .075/4)^4t, solve for t

8/5 = 1.6 = (1.01875)^4t

t = about 6.32 years

= about 6 years and 3.9 months

log_1.018751.6 = 4t

=ln1.6/ln1.01875 = about 25.3

4t = 25.3

t = 6.3 years