MTH302

Assignment -1

Question: 1
If the Basic salary of an employee is Rs. 55000 and Allowances are Rs. 6000.
  • What is the cost of the company on account of leaves? If casual leaves are 24 and sick leaves are12 per year and normal working days per month are 22.  
Solution
Gross salary = Basic salary + Allowances
Gross salary = 55000 + 6000 = 61000 Rs
Per day cost = Gross salary / working days per month
Per day cost = 61000/22 = 2772.73 Rs
Casual leaves = 2772.73 * 24 = 66545.5 Rs
Sick Leaves = 2772.73 * 12 = 33272.7
Total cost of leaves = Casual leaves + Sick Leaves
Total cost of leaves = 66542.5 + 33272.7
Total cost of leaves = 99815.2 Rs

Question: 2

 If you want to get a loan but can only afford to pay Rs.13, 000 per month. How much can you borrow (loan amount) if the interest rate is 5% annually for 30 years?

Solution

PV = C * [1 - (1+i)-n / i ]
i = 5% per year = 0.05
i = 0.05/12 per month = 0.004167
n = Total no of installment = 30 * 12 =360
C = 13000
PV = C * [1 - (1+i)-n / i ]
PV = 13000 * [1 - (1+0.004167)-360 / 0.004167 ]
PV = 13000 * [(1 – 0.2238) / 0.004167]
PV = 13000 * 186.27
PV = 2421550.27

you can borrow (loan amount) 2421550 Rs


Question: 3                                                                                                     
Suppose you invest Rs. 5000 at the end of each year for 8 years in an account that pay interest at 8%, compounded annually. How much money would you have in the account at the end of the eight years?


Solution
FV = C * [(1+i)n - 1 / i ]
C = 5000
i = 8% = 0.08
n = 8
FV = C * [(1+i)n - 1 / i ]
FV = 5000 * [(1+0.08)8 - 1 / 0.08 ]
FV = 5000 * [1.851 - 1 / 0.08 ]
FV = 5000 * [0.851 / 0.08 ]
FV = 5000 * 10.6375
FV = 53187.5
you have in the account at the end of the eight years 53187 Rs




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