Answer:
Results are below.
Explanation:
Giving the following information:
Initial investment= $6,000
To calculate the future value, we need to use the following formula:
FV= PV*(1+i)^n
Compounded annually:
n= 20
i= 0.035
FV= 6,000*1.035^20
FV= $11,938.73
Compounded semi-annually:
n=20*2= 40
i= 0.035/2= 0.0175
FV= 6,000*(1.0175^40)
FV= $12,009.58
Compounded quarterly:
n= 20*4= 80
i= 0.035/4= 0.00875
FV= 6,000*(1.00875^80)
FV= $12,045.78
Compounded monthly:
n= 20*12= 240
i= 0.035/12= 0.00292
FV= 6,000*(1.00292^240)
FV= $12,079.84
Compounded weekly:
n= 20*52= 1,040
i= 0.035/52= 0.000673
FV= 6,000*(1.000673^1,040)
FV= $12,078.71
Compounded daily:
n= 20*365= 7,300
i= 0.035/365= 0.000096
FV= 6,000*(1.000096^7,300)
FV= $12,091.78
Answer:
P = $6000
i = 3.5% = 0.035
n =20
Future value = P*(1+i/m)^nm
If compounded annually = 6,000*(1+0.035) ^20 = 6,000*(1.035)^20 = 6,000*1.9898 = $11938.80
If compounded semi-annually = 6,000*(1+0.035/2)^20*2 = 6,000*(1+0.0175)^40 = 6,000*(1.0175)^40 = 6,000*2.00159734319 = $12009.58405914 = $12009.58
If compounded quarterly = 6,000*(1+0.035/4)^20*4 = 6,000*(1+0.00875)^80 = 6,000*(1.00875)^80 = 6,000* 2.00763065501 = $12045.78393006 = $12045.78
If compounded monthly = 6,000*(1+0.035/12)^20*12 = 6,000*(1+0.0029167)^240 = 6,000*(1.0029167)^240 = 6,000 * 2.01171808178 = $12070.30849068 = $12070.31
If compounded weekly = 6,000*(1+0.035/52)^20*52 = 6,000*(1.00067307692)^1040 = 6,000 * 2.01327857595 = $12079.6714557 = $12079.67
If compounded daily = 6,000*(1+0.035/365)^20*365 = 6,000*(1.00009589041)^7300 = 6,000*2.01368511398 = $12082.11068388 = $12082.11
