Find the time required for an investment of 5000 dollars to grow to 7600 dollars at an interest rate of 5.5% per year, compounded quarterly. Round to the nearest year.

Answer 1

7600=5000(1+.055/4)^4t

76/50 = 1.01375^4t

38/25 = 1.01375^4t

log_1.01375(38/25) = 4t

t = ln(38/25)/4ln1.01375

= 7.66513483 years to reach $7600 with $5000 with 5.5% compounded quarterly

= about 7 2/3 years

= 8 years, rounded to nearest year