Assignment no. 1 MTH 302 Spring 2022 Maximum Marks: 15 Due Date: 13 June, 2022

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 Assignment no. 1                                   MTH 302                                Spring 2022

Maximum Marks: 15                                                                 Due Date: 13 June, 2022

QUESTION NO. 1:-

A deposit of Rs. 6000 in a bank account earns interest 5% compounded monthly for four years. How much amount is accumulated in the account after 4 years?

Solution:-

We know that:

Balance formula:

{\rm{New balance formula }} = {\rm{ A }} = P{\left[ {1 + \frac{r}{n}} \right]^{nt}}\,\,\,\,\,\,\,\,\,\,\, \to (a)

Given value:

                                   r = 5%  

                                     = 0.05

                                   P = 6000 Rs.

                                   t = 4 years

                                   n = 12

                                   A =?

Now,

Putting values in eq. (a).


{\rm{New balance formula }} = {\rm{ A }} = P{\left[ {1 + \frac{r}{n}} \right]^{nt}}\,

{\rm{New balance formula }} = {\rm{ A }} = \left( {6000} \right){\left[ {1 + \frac{{0.05}}{{12}}} \right]^{(12)(4)}}\,\,

{\rm{New balance formula }} = {\rm{ A }} = \left( {6000} \right){\left[ {\frac{{12 + 0.05}}{{12}}} \right]^{48}}

{\rm{New balance formula }} = {\rm{ A }} = \left( {6000} \right){\left[ {\frac{{12.05}}{{12}}} \right]^{48}}\,\,\,

{\rm{New balance formula }} = {\rm{ A }} = \left( {6000} \right){\left[ {1.0041666666.....} \right]^{48}}

{\rm{New balance formula }} = {\rm{ A }} = \left( {6000} \right){\left[ {1.0042} \right]^{48}}\,

{\rm{New balance formula }} = {\rm{ A }} = \left( {6000} \right)\left( {1.2228422} \right)

{\rm{New balance formula }} = {\rm{ A }} = 7337.053202

{\rm{New balance formula }} = {\rm{ A }} = 7337.0532

QUESTION NO. 2:-

A 55-inch segment is divided in to three parts whose lengths have the ratio 2 : 4 : 5. What is the length of the longest part?

Solution:-

Total length of segment = 55 inch

Ratio = 2 : 4 : 5

Sum of ratio = 2 + 4 + 5

                       = 11

Longest part =?

The highest value in ratio is 5.

We know that:

Longest part = (highest value in ratio/ Sum of ratio) x Total length of segment

Longest part = (5/11) x (55) inch

Longest part = (5 x 5) inch

Longest part = 25 inch

QUESTION NO. 2:-

Suppose that you establish an IRA (Individual Retirement Account) at age 43 and you will retire after 22 years hence at age 65. You plan to make annual payments of Rs1000 in to the IRA (Individual Retirement Account) at the beginning of each year. If you assume a rate of return of 8.5 percent a year, calculate the future value of your IRA (Individual Retirement Account) when you will retire at age 65.

 Solution:-

Payment per period = C = 1000Rs.

Interest rate = i = 8.5%

                             = 0.085

Number of payment = 22

We know that:

Formula;-

{\rm{Future value }} = C\, \times \,\left[ {\frac{{{{\left( {1 + i} \right)}^n} - 1}}{i}} \right]

{\rm{Future value }} = (1000)\, \times \,\left[ {\frac{{{{\left( {1 + 0.085} \right)}^{22}} - 1}}{{0.085}}} \right]

{\rm{Future value }} = (1000)\, \times \,\left[ {\frac{{{{\left( {1.085} \right)}^{22}} - 1}}{{0.085}}} \right]

{\rm{Future value }} = (1000)\, \times \,\left[ {\frac{{(6.018028499...) - 1}}{{0.085}}} \right]

{\rm{Future value }} = (1000)\, \times \,\left[ {\frac{{6.0180 - 1}}{{0.085}}} \right]

{\rm{Future value }} = (1000)\, \times \,\left[ {\frac{{5.0180}}{{0.085}}} \right]

{\rm{Future value }} = (1000)\, \times \,(59.03529412)

{\rm{Future value }} = (1000)\, \times \,(59.0352)

{\rm{Future value }} = \,59035.2





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