B How much should she invest now at 6%, compounded quarterly, so that she will have enough to buy a new car

Question

Barbara knows that she will need to buy a new car in 4 years. The car will cost $15,000 by then. How much should she invest now at 6%, compounded quarterly, so that she will have enough to buy a new car

Answer 1

P = B/(1+r/n)^nt    

 

B = ending balance= $15000      

r=rate= .06  

t=number of years=4  

n=number of times interest is compounded in a year=4 times per year

 

So   (1+.06/4)^4*4  =  (1+.015)¹⁶  =  (1.015)¹⁶ = 1.26899

 

P = 15000/1.26899 = $11820

 

P = $11820