help soliving please

Question

If 47,600 dollars is invested at an interest rate of 9 percent per year, find the value of the investment at the end of 5 years for the following compounding methods. Round to the nearest cent.

(a) Annually:

Your answer is   

(b) Monthly:

Your answer is   

(c) Daily:

Your answer is   

(d) Continuously:

Your answer is   

Answer 1

for continuous compounding

A=Pe^rt

A = 47,600e^.09(5)

= $74,651.66 at the end of 5 years at 9% annual interest

for other compounding

A=P(1+r/n)^nt

A =47,600(1 +.09/n)^5n where n= 365 for daily compounding, n=12 for monthly compounding, n=1 for annual compounding,

annual compounding

A =47,600(1.09)^5

A = $73,238.50

monthly compounding

A= 47,600(1 + .09/12)^12(5)

A = 47,600(1+.0075)^60

A = 47600(1.0075)^60

A =$74,526.42

daily compounding

A= 47600(1+.09/365)^365(5)

A=47600(1.0002465753425)^1825

A= $74,647.52

A=very close to the same as continuous compoundin, just $4.14 less

n= infinity for continuous compounding so the formula collapses to a limit as n approaches infinity