Question

If $36,500 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) annually
$  

(b) semiannually
$  

(c) quarterly
$  

(d) monthly
$  

(e) daily (N = 360)
$  

(f) every minute (N = 525,600)
$  

(g) continuously
$  

(h) simple (not compounded)
$

Answer 1

(a)

the future value

=PV*(1+(r/m))^(n*m)

where m is number of compounding periods in a year

=36500*(1+(6.8%/1))^(30*1)

=262,682.08

(b)

the future value

=PV*(1+(r/m))^(n*m)

where m is number of compounding periods in a year

=36500*(1+(6.8%/2))^(30*2)

=271,347.10

(c)

the future value

=PV*(1+(r/m))^(n*m)

where m is number of compounding periods in a year

=36500*(1+(6.8%/4))^(30*4)

=275,935.27

(d)

the future value

=PV*(1+(r/m))^(n*m)

where m is number of compounding periods in a year

=36500*(1+(6.8%/12))^(30*12)

=279,095.50

(e)

the future value

=PV*(1+(r/m))^(n*m)

where m is number of compounding periods in a year

=36500*(1+(6.8%/360))^(30*360)

=280,653.16

(f)

the future value

=PV*(1+(r/m))^(n*m)

where m is number of compounding periods in a year

=36500*(1+(6.8%/525600))^(30*525600)

=280,707.20

(g)

the future value in case of continuously compouding

=PV*e^(r*n)

=36500*e^(6.8%*30)

=36500*exp(6.8%*30) here exp is the excel function=exp(number)

=280,707.24

(h)

the future value

=invested amount+interest earned

=invested amount+(invested amount*rate of interest*number of years)

=36500+(36500*6.8%*30)

=110,960.00

the above is answer..