Question

Andrea Deposits $1000 into a savings account today. The annual interest rate is 10%, but compounds semi-annually. How many years will it take for her money to grow to $4,356,561?

Answer 1

future amount = amount deposited*(1+r)^n

here,

future amount = 4356561

amount deposited =1000

interest rate = 10% per annum =>10*6/12=>5% for semi annual period =>0.05

n = total number of semi annual periods = to be found out.

=>1000*(1+0.05)^n=4356561

=>(1.05)^n=4,356.561.

apply logarithms on both sides.

=> n log (1.05) = log (4356.561)

=>n*0.0211893 =3.6391438

=>n=171.744409..........(these are semi annual periods)

so number of years = 171.744409 / 2 semi annual periods per year

=>85.87 years.or 86 years to round off.