1 If you need 50000 six years from now what is the minimum a

1) If you need $50,000 six 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)?

2. An investment grows by 25% over a 20 year period. What is its effective annual percent growth rate?

Solution

1)A = P(1 + r/n)^nt ,A is the amount after t years=50000.

P is the principal,

r is the annual rate of interest=3%=0.03,

t=number of years =6

n= number of periods

a)annually

n=1

50000= P(1 + 0.03/1)^1*6

P=50000/(1.03)⁶

P=41874.21$

amount of money you need to deposit into a bank account=41874.21$

b)monthly

n=12

50000= P(1 + 0.03/12)^12*6

P=50000/(1.0025)⁷²

P=41772.89$

amount of money you need to deposit into a bank account=41772.89$

c)daily

n=365

50000= P(1 + 0.03/365)^365*6

P=50000/(1.00008291)²¹⁹⁰

P=41772.89$

amount of money you need to deposit into a bank account=41763.82$