Question 1193454: Find the rate compounded semi-annually if 30,000 is the present value
of 55,000 due at the end of 4 years. Found 2 solutions by Theo, MathTherapy:Answer by Theo(13342) (Show Source): You can put this solution on YOUR website! present value is 30,000
future value is 55,000
time period is 4 years * 2 semi-annual periods per year = 8 semi-annual time periods.
formula is f = p * g ^ n
f is the future value
p is the present value
g is the growth factor per time period
n is the number of time periods.
formula becomes:
55,000 = 30,000 * g ^ 8
divide both sides of the equation by 30,000 to get:
55,000 / 30,000 = g ^ 8
simplify a little to get:
55/30 = g ^ 8
take the 8th root of both sides of the equation to get:
(55/30)^(1/8) = g
solve for g to get:
g = 1.078711179 per semi-annual period.
since g = 1 + r, solve for r to get:
r = g - 1 = .078711179 per semi-annual period.
multiply by 2 to get .1574223574 per year.
multiply by 100 to get 15.74223574% per year.
that is the annual rate compounded semi-annually that will get 30,000 to grow to 55,000 at the end of 4 years.
to solve the problem, you divide that rate by 2 to get the rate per semi-annual period and you multiply the number of years by 2 to get the number of semi-annual periods.