2. Jim started a systematic investment program by buying $250.00 worth of mutual funds on the first day of every month starting on March 1.
Mutual funds are purchased in units. Jim purchased as many units as he could with his $250.00, including fractions of units. Unit prices for the first six months were $9.00, $9.20, $10.75, $8.50, $8.40, and $11.15 respectively. Complete parts (a) through (d) below.
To complete parts (a) through (d) of the question, we need to calculate the following:
(a) The number of units Jim purchased each month
(b) The total value of Jim's investment each month, based on the number of units purchased and the unit price
(c) The total amount Jim invested over the six-month period
(d) The average unit price Jim paid over the six-month period
Let's calculate each of these parts step by step:
(a) Number of units purchased each month:
To calculate the number of units Jim purchased each month, we divide the amount he invested by the unit price for that month.
Month 1 (March 1):
Number of units purchased = $250 / $9.00 = 27.78 (rounded to 2 decimal places)
Month 2 (April 1):
Number of units purchased = $250 / $9.20 = 27.17 (rounded to 2 decimal places)
Month 3 (May 1):
Number of units purchased = $250 / $10.75 = 23.26 (rounded to 2 decimal places)
Month 4 (June 1):
Number of units purchased = $250 / $8.50 = 29.41 (rounded to 2 decimal places)
Month 5 (July 1):
Number of units purchased = $250 / $8.40 = 29.76 (rounded to 2 decimal places)
Month 6 (August 1):
Number of units purchased = $250 / $11.15 = 22.37 (rounded to 2 decimal places)
(b) Total value of Jim's investment each month:
To calculate the total value of Jim's investment each month, we multiply the number of units purchased by the unit price for that month.
Month 1 (March 1):
Total value of investment = 27.78 (units purchased) * $9.00 (unit price) = $250.02
Month 2 (April 1):
Total value of investment = 27.17 (units purchased) * $9.20 (unit price) = $250.24
Month 3 (May 1):
Total value of investment = 23.26 (units purchased) * $10.75 (unit price) = $250.01
Month 4 (June 1):
Total value of investment = 29.41 (units purchased) * $8.50 (unit price) = $249.94
Month 5 (July 1):
Total value of investment = 29.76 (units purchased) * $8.40 (unit price) = $249.98
Month 6 (August 1):
Total value of investment = 22.37 (units purchased) * $11.15 (unit price) = $249.99
(c) Total amount Jim invested over the six-month period:
To calculate the total amount Jim invested over the six-month period, we sum up the total value of his investment each month.
Total amount invested = $250.02 + $250.24 + $250.01 + $249.94 + $249.98 + $249.99 = $1500.18
(d) Average unit price Jim paid over the six-month period:
To calculate the average unit price Jim paid over the six-month period, we divide the total amount invested by the total number of units purchased.
Total number of units purchased = 27.78 + 27.17 + 23.26 + 29.41 + 29.76 + 22.37 = 159.75
Average unit price = Total amount invested / Total number of units purchased = $1500.18 / 159.75 = $9.39 (rounded to 2 decimal places)
So, the answers to parts (a) through (d) are as follows:
(a) Number of units purchased each month: 27.78, 27.17, 23.26, 29.41, 29.76, 22.37
(b) Total value of Jim's investment each month: $250.02, $250.24, $250.01, $249.94, $249.98, $249.99
(c) Total amount Jim invested over the six-month period: $1500.18
(d) Average unit price Jim paid over the six-month period: $9.39
a) Calculate the number of units Jim purchased on each of the first six months.
To calculate the number of units Jim purchased, we need to divide the amount invested each month by the respective unit price.
Month 1 (March):
Units purchased = $250.00 / $9.00 = 27.78 units (rounded to 2 decimal places)
Month 2 (April):
Units purchased = $250.00 / $9.20 = 27.17 units (rounded to 2 decimal places)
Month 3 (May):
Units purchased = $250.00 / $10.75 = 23.26 units (rounded to 2 decimal places)
Month 4 (June):
Units purchased = $250.00 / $8.50 = 29.41 units (rounded to 2 decimal places)
Month 5 (July):
Units purchased = $250.00 / $8.40 = 29.76 units (rounded to 2 decimal places)
Month 6 (August):
Units purchased = $250.00 / $11.15 = 22.42 units (rounded to 2 decimal places)
b) Calculate the total number of units Jim purchased during the first six months.
To calculate the total number of units Jim purchased, we sum up the units purchased for each month.
Total units purchased = 27.78 + 27.17 + 23.26 + 29.41 + 29.76 + 22.42 = 160.80 units (rounded to 2 decimal places)
c) Calculate the average unit price for the first six months.
To calculate the average unit price, we need to find the average of the unit prices for the first six months.
Average unit price = (9.00 + 9.20 + 10.75 + 8.50 + 8.40 + 11.15) / 6 = 9.4583 (rounded to 4 decimal places)
d) Calculate the value of Jim's mutual fund holdings at the end of the six months if the unit price increased to $11.25.
To calculate the value of Jim's holdings, we need to multiply the total number of units purchased by the updated unit price.
Value of Jim's holdings = Total units purchased * Updated unit price
= 160.80 units * $11.25 = $1,809.00
(a) How many units of the mutual fund did Jim purchase on April 1?
To calculate the number of units Jim purchased on April 1, we need to determine the unit price on that day first.
From the information given, we know that the unit price on April 1 is $9.20. This means that Jim has $250 worth of funds to invest and the unit price is $9.20 per unit. To find the number of units, we divide the total investment amount by the unit price.
Number of units purchased on April 1 = Investment amount / Unit price
= $250 / $9.20
≈ 27.17 units (rounded to two decimal places)
Therefore, Jim purchased approximately 27.17 units of the mutual fund on April 1.
(b) What is the total amount Jim invested in the first six months?
To find the total amount Jim invested in the first six months, we need to multiply the monthly investment amount by the number of months (6).
Monthly investment amount = $250
Number of months = 6
Total amount invested = Monthly investment amount x Number of months
= $250 x 6
= $1,500
Therefore, Jim invested a total of $1,500 in the first six months.
(c) What is the average unit price for the first six months?
To find the average unit price for the first six months, we need to calculate the total value of the units purchased and divide it by the total number of units.
Total value of units purchased = Sum of (Number of units purchased x Unit price) for each month
= (27.17 x $9.00) + (27.17 x $9.20) + (27.17 x $10.75) + (27.17 x $8.50) + (27.17 x $8.40) + (27.17 x $11.15)
Next, we need to calculate the total number of units purchased.
Total number of units purchased = Number of units purchased per month x Number of months
= 27.17 x 6
Finally, we can calculate the average unit price.
Average unit price = Total value of units purchased / Total number of units purchased
For simplicity, let's calculate the total value of units purchased and the total number of units first.
Total value of units purchased = (27.17 x $9.00) + (27.17 x $9.20) + (27.17 x $10.75) + (27.17 x $8.50) + (27.17 x $8.40) + (27.17 x $11.15)
= $1,329.66
Total number of units purchased = 27.17 x 6
= 163.02 units
Average unit price = $1,329.66 / 163.02 units
≈ $8.15 (rounded to two decimal places)
Therefore, the average unit price for the first six months is approximately $8.15.
(d) What is the dollar value of Jim's investment on September 1?
To determine the dollar value of Jim's investment on September 1, we need to know the unit price on that day.
From the information given, we know that the unit price on September 1 is $11.15. This means that Jim has a certain number of units, and each unit is worth $11.15. To find the dollar value of his investment, we multiply the number of units by the unit price.
Number of units purchased on September 1 = Total investment amount / Unit price
= $250 / $11.15
≈ 22.37 units (rounded to two decimal places)
Dollar value of Jim's investment on September 1 = Number of units purchased on September 1 x Unit price
= 22.37 units x $11.15
≈ $249.65 (rounded to two decimal places)
Therefore, the dollar value of Jim's investment on September 1 is approximately $249.65.