If you need $30,000 four years from now, what is the minimum amount of money you need to deposit into a bank account that pays 3% annual interest, compounded (give your answers to the nearest cent):

Question

 If you need $30,000 four years from now, what is the minimum amount of money you need to deposit into a bank account that pays 3% annual interest, compounded (give your answers to the nearest cent):

(a) annually? $  

(b) monthly? $  

(c) daily (assuming 365 days in a year)? $ 

Answer 1

(a) 30000 ≤ p(1.03)³

(b) 30000 ≤ p(1 + 0.03/12)^(3)(12)

(c) 30000 ≤ p(1 + 0.03/365)^(3)(365)

Answer 2

(a) 30000 ≤ p(1.03)³

30000/(1.03)³ ≤ p

27454.25 ≤ p

(b) 30000 ≤ p(1 + 0.03/12)^(3)(12)

30000/((1 + 0.03/12)^(3)(12) ≤ p

27421.02 ≤ p

(c) 30000 ≤ p(1 + 0.03/365)^(3)(365)

30000^/(1 + 0.03/365)^(3)(365) ≤ p

27418.04 ≤ p

a 27454.25

b 27421.02

c 27418.04