If $3,000 is invested at 7%, find the value of the investment after 5 years if interest is compounded as follows. (Round your answers to the nearest cent.)

Answer 1

Given: $3000 invested at 7%

Find: Value after 5 years for various compounding.

Solution:

r = rate = 7% = .07

n = years = 5

c = compounding periods per year

A0 = Initial investment = 3000

An = Value after n years

An = A0(1 + r/c)^(c*n)

A5 = (3000)*(1 + .07/4)^(4*5) Compounded quarterly: c = 4

A5 = (3000)*(1.0175)^20

A5 = 4244.34

A5 = (3000)*(1 + .07/12)^(12*5) Compounded monthly: c = 12

A5 = (3000)*(1.0058)^60

A5 = 4252.88

A = Pe^(rt) Compounded continuously (standard eqn.)

An = A0*e^(r*n) Using our variables

A5 = (3000)*e(.07*5) Using given values

A5 = 4257.20 Compounded continuously: c = infinity