Question

How much will $6000 be worth if it is invested at 3.5% interest for 20 years compounded annually, semi-annually, quarterly, monthly, weekly, daily?

Answer 1

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

Answer 2

Results are below.

Step-by-step 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