MTH302

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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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