Question 838191
each van costs 24,800
6 new vans will cost 24,800 * 6 = 148,800.


the number of years is 4.
the number of compounding periods per year is 4 (quarterly).
the number of time periods involved is therefore 4 * 4 = 16 quarterly time periods.


the annual interest rate is 12%.
if you pay interest rate quarterly, then the quarterly interest rate is 12% / 4 = 3% per quarter.


the decimal equivalent of 3% is .03


the formula you will use is:


f = p * (1 + r) ^ n


f is equal to the amount of money you will be paying for the vans in 4 years.
p is the amount of money you will need to today in order to do that.
r is equal to the quarterly compounding rate which is equal to .03.
n is equal to the number of quarterly compounding periods which is equal to 16.


the formula becomes:


148,800 = p * (1 + .03) ^ 16


this can be written as:


148800 = p * (1.03)^16


divide both sides of this equation by (1.03)^16 and you get:


148800 / (1.03)^16 = p


simplify to get:


148800 / 1.604706439 = p


simplify further to get:


p = 92727.24056


this can be written as:


p = $92,727.25 rounded to the next highest penny.


you will need to invest $92,727.25 today in order to have at least $148,800 in 4 years.


$92,727.25 invested at 3% per quarter for 16 quarters comes out to be:


92727.25 * (1.03)^16 which is equal to 148800.0152  which can be written as:


$148,800.02 rounded to the nearest penny.


your answer would be selection a which is 92727.