Question

If $35,500 is invested at 6.8% for 30 years, find the future value if the interest is compounded the following ways. (Round your answers to the nearest cent.)

(a) Semiannually

(b)monthly

(c)daily (n=360)

(d) continuously

Answer 1

If $35,500 is invested at 6.8% for 30 years, find the future value if the interest is compounded the following ways. (Round your answers to the nearest cent.)

Future Value = Present Value*(1+Rate/n)^m

n = number of compounding period in a year

m = n x total years

(a) Semiannually

n = 2, m = 2 x 30 = 60

Future Value = 35500*(1+6.8%/2)^60 = $263,912.94

(b)monthly

n = 12; m = 12 x 30 = 360

Future Value = =35500*(1+6.8%/12)^360 = $271,449.04

(c)daily (n=360)

n = 360 ; m = 360 x 30 = 10800

Future Value = 35500*(1+6.8%/360)^10800 = $272,964.04

(d) continuously

Exponential value = 2.718281828; m = 30

Future Value = Present Value*exponential value^(Rate*m)

Future Value = 35500*2.718281828^(6.8%*30) = $273,016.63