Answer:
1)
Option 3 was the least amount invested and The investment plan was single amount
2)
option 2 yielded the highest amount at the end of the 30 years, The basis of the plan is contributions are made at the beginning of the period and $75/ quarter at a rate of 4.00%
3)
Principal invested for the highest final balances = $ 17425.43
Principal invested for the lowest final balances = $ 6489.17
Difference = $ 10,936.26
Difference in the interest earned = Interest earned in 2nd option - Interest earned on 3rd option
Difference in the interest earned = 8425.43 - 5489.17
Difference in the interest earned = $ 2936.26
4)
It is better to invest more money in the beginning as it yield more ( Total Interest earned = 6209.31)
Step-by-step explanation:
Options Contributions Total Interest Earned Final Balance
1 $25/ month 6,250.50 15,250.50
2 $75/ quarter 8,425.43 17,425.43
3 $ 1000 5,489.17 6,489.17
Which option was the least amount invested and what was the investment plan?
Option 3 was the least amount invested and The investment plan was single amount
Which option yielded the highest amount at the end of the 30 years and what was the basis of the plan?
option 2 yielded the highest amount at the end of the 30 years, The basis of the plan is contributions are made at the beginning of the period and $75/ quarter at a rate of 4.00%
What is the difference in the principal invested for the highest and lowest final balances? What is the difference in the interest earned?
Principal invested for the highest final balances = $ 17425.43
Principal invested for the lowest final balances = $ 6489.17
Difference = $ 10,936.26
Difference in the interest earned = Interest earned in 2nd option - Interest earned on 3rd option
Difference in the interest earned = 8425.43 - 5489.17
Difference in the interest earned = $ 2936.26
Is it better to invest more money in the beginning or the end of the 30 years?
It is better to invest more money in the beginning as it yield more
The plan you would recommend for the largest return on investment (this means the most interest for the least amount invested)
Option 1
Amount Invested = 25*12*30 = 9000
if contributions are made at the beginning of the period
Amount at the end of 30 Year = fv(rate,nper,pmt,pv,1)
rate = 3.25% compounded monthly = 3.25%/12
nper = 30 year = 30*12 = 360
pmt = 25
pv = 0
Amount at the end of 30 Year = fv(3.25%/12,360,25,0,1)
Amount at the end of 30 Year = $ 15,250.50
Total Interest earned = Amount at the end of 30 Year - Amount invested
Total Interest earned = 15250.50 - 9000
Total Interest earned = 6250.50
if contributions are made at the end of the period
Amount at the end of 30 Year = fv(rate,nper,pmt,pv,0)
rate = 3.25% compounded monthly = 3.25%/12
nper = 30 year = 30*12 = 360
pmt = 25
pv = 0
Amount at the end of 30 Year = fv(3.25%/12,360,25,0,0)
Amount at the end of 30 Year = $ 15,209.31
Total Interest earned = Amount at the end of 30 Year - Amount invested
Total Interest earned = 15209.31 - 9000
Total Interest earned = 6209.31
Option 2
Amount Invested = 75*4*30 = 9000
if contributions are made at the beginning of the period
Amount at the end of 30 Year = fv(rate,nper,pmt,pv,1)
rate = 4% compounded quarterly = 4%/4 = 1%
nper = 30 year = 30*4 = 120
pmt = 75
pv = 0
Amount at the end of 30 Year = fv(1%,120,75,0,1)
Amount at the end of 30 Year = $ 17425.43
Total Interest earned = Amount at the end of 30 Year - Amount invested
Total Interest earned = 17425.43 - 9000
Total Interest earned = 8425.43
if contributions are made at the end of the period
Amount at the end of 30 Year = fv(rate,nper,pmt,pv,0)
rate = 4% compounded quarterly = 4%/4 = 1%
nper = 30 year = 30*4 = 120
pmt = 75
pv = 0
Amount at the end of 30 Year = fv(1%,120,75,0,0)
Amount at the end of 30 Year = $ 17,252.90
Total Interest earned = Amount at the end of 30 Year - Amount invested
Total Interest earned = 17252.90 - 9000
Total Interest earned = 8252.90
Option 3
Amount Invested = 1000
Amount at the end of 30 Year = fv(rate,nper,pmt,pv,1)
rate = 6.25% compounded monthlyy = 6.25%/12
nper = 30 year = 30*12 = 360
pmt = 0
pv = 1000
Amount at the end of 30 Year = fv(6.25%/12,360,0,1000)
Amount at the end of 30 Year = $ 6489.17
Total Interest earned = Amount at the end of 30 Year - Amount invested
Total Interest earned = 6489.17-1000
Total Interest earned = 5489.17
