An investment of 8000 is made on April 19 2004 Find the valu

An investment of $8,000 is made on April 19, 2004. Find the value of this investment at the end of April 19, 2016 in each of the following situations. For full credit show all relevant equations and give your answers accurate to two decimal places. (a.) At an annual interest rate of 3% compounded monthly. (b.) At an annual interest rate of 3% compounded daily. (c.) At an annual interest rate of 3% compounded continuously.

Solution

r = 3% P = $8000, t = 12 yrs

(a.) At an annual interest rate of 3% compounded monthly.

A = P(1 +r/12)^(12t)

= 8000( 1+0.03/12)^144

= 8000*1.43 = $ 11461.48

(b.) At an annual interest rate of 3% compounded daily.

A = P(1 + r/365)^(365t)

= 8000( 1+ 0.03/365)^(12*365)

= $11466.46

(c.) At an annual interest rate of 3% compounded continuously.

A = Pe^(rt) = 8000e^(0.03*12) = 8000*1.433 =$ 11466.40