MTH302 Assignment solution

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