Question

If $17,000 is invested at 4.5% 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) annually:

FV = P ( 1+r/N)^N

FV = 17000 * (1+0.045)^30

FV = 17000 *3.745318 = 63670.41

b) semiannually:

FV = P ( 1+r/N)^N

FV = 17000 * (1+0.045/2)^(2*30)

FV = 17000 * (1.0225)^60

FV = 17000 * 3.800135 = 64602.3

c) quarterly:

FV = P ( 1+r/N)^N

FV = 17000 * (1+0.045/4)^(4*30)

FV = 17000 * (1.01125)^120

FV = 17000 * 3.82846 = 65083.82

d) monthly:

FV = P ( 1+r/N)^N

FV = 17000 * (1+0.045/12)^(12*30)

FV = 17000 * (1.00375)^360

FV = 17000 * 3.84769805 = 65410.87

e) daily:

FV = P ( 1+r/N)^N

FV = 17000 * (1+0.045/360)^(360*30)

FV = 17000 * (1.000125)^10800

FV = 17000 * 3.8571001 = 65570.70

f) every minute:

FV = P ( 1+r/N)^N

FV = 17000 * (1+0.045/525600)^(525600*30)

FV = 17000 * (1.000000085)^15768000

FV = 17000 * 3.8201127653 = 64941.92

g) continuously:

FV = P * e^rt

FV = 17000 * e^(0.045*30)

FV = 17000 * e^1.35

FV = 17000 * 3.8574255307 = 65576.23

h) Simple:

FV = P + (PRT)

FV = 17000 + ( 17000*0.045*30) = 39950