Depreciation and Value

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Task 1
i. After knee surgery, your trainer tells you to return to your jogging program slowly. He suggests jogging for 12 minute each day for the first week. Each week thereafter, he suggests that you increase that time by 6 minutes per day. How many weeks will it be before you are up to jogging 60 minutes per day? Solution:

(12, 18, 24, 30…… 60)
T1 = 12, T2 = 18, T3=24, T4 = 30, Tn = 60
T2 – T1 = T3 – T2
18 – 12 = 24 – 18
6 = 6
This above is arithemetic sequence.
Common difference (d) = 6
First term (a) = 12
Tn = a + (n – 1) d
60 = 12 + (n – 1) 6
60 = 12 + 6n – 6
60 = 6n + 6
n = 9
*The week that I can jog 60 minutes in a day is ninth weeks. Therefore, it would be eight weeks before I am up to jogging 60 minutes per day.

ii. A culture of bacteria doubles every 2 hours. If there are 500 bacteria at the beginning, how many bacteria will there be after 24 hours? Solution:
500, 1000, 2000, 4000……
Start 2hours, 4hours, 6hours
T1 = 2, T 2 = 4, T3=6 T1 = 500, T2 = 1000, T3= 2000, T4 = 4000 T2 – T1 = T3 – T2 T2T1=T3T2
4 – 2 = 6 – 4 1000500=20001000
2 = 2 2 = 2
This above is arithemetic sequence. This above is geometric sequence. Common difference (d) = 2 Common ratio (r) = 2
First term (a) = 2 First term (a) = 500 Tn = 24 Tn = 12
Tn = a + (n – 1) d Tn = arn-1
24 = 2 + (n – 1) 2 T12 = 500(2)12-1 24 = 2 + 2n – 2 T12 = 500(2)11
2n = 24 – 2 + 2 T12 = 500 × 2048
2n = 24 T12 = 1024 000
n = 12

Therefore, if there are 500 bacteria at the beginning, 1024 000 bacteria will there be after 24 hours.

Task 2
i. What is the different between trade discount and cash discount? * Trade discounts are payments to distribution channel members for performing some function. For example if Sara had a warehouse, stocked my goods in Sara warehouse, and then shipped my goods to my customers for me. Sara would offer me an invoice with her trade discounts. The discounts could be 10/15/10 Net 30. In the example 10% could indicate a 10% discount for warehousing the product, an additional 15% discount for shipping the product, and an additional 10% discount for keeping her shelves stocked. * Cash discount is in most cases they are offered to a business's customer as an incentive to pay the bill faster. For example, 3% 15 days net 30. If the customer pays the invoice in 15 days they will receive a 3% discount from the invoice. ii. On 20th January 2006, Mr. A bought some goods at $100 000 with cash discount term 3/10, n/30. To pay the invoice on 30th January, she borrowed the money for 20 days at 10% per annum simple interest. How much did she save by borrowing to take advantage of the discount? Solution:

20th January to 30th January = 10days
Net price = RM 100,000
Since, the invoice was paid 10 days after the date of the invoice, so the cash discount offered 3%. Cash discount = Discount rate × Net price
= 0.03 × 100 000
= RM3 000
P = RM100 000 Simple interest = 100 000 × 0.10 × 0.56 R = 10% = RM5 600 T =20 days= 2030=0.56 Simple amount = RM100 000 - RM5 600 = RM105 600 Task 3

i. Alan decides to set aside $50 at the end of each month for his child’s college education. If the child were to be born today, how much will be available for its college education when s/he turns 19 years old Assume an interest rate of 5% compounded monthly. Solution:

R = $50 S=R[(1+i)n-1i] n = 18 years =50[1+5%12)216-15%12 ] = 18 × 12 =50[(2.4550-1)0.004166 ]...
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