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Basics of Financial Mathematics Test 20

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Basics of Financial Mathematics Test 20
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  • Question 1
    1 / -0
    The price of a new car is Rs. $$2500$$. The price depreciates by $$12\%$$ each year (p.a). Find its value at the end of $$3$$ years.
    Solution
    Given, $$P = 2500, r = 12\%, n = 3$$ years
    We know, $$A = P\left [\left (1-\dfrac{r}{100}\right)^n\right]$$
    $$\Rightarrow A = 2500\left [\left (1-\dfrac{12}{100}\right)^3\right]$$
    $$\Rightarrow A =$$ Rs. $$1703.68$$
    Thus, the value of a car at the end of $$3$$ years is Rs. $$1703.68$$.
  • Question 2
    1 / -0
    The population of an invasive species of moth doubles every $$5$$ years. If the initial population is $$300$$, what will be the population after $$15$$ years?
    Solution
    Population of an invasive species of moth doubles every $$5$$ years.
    Let the initial population be $$x$$
    So after $$5$$ years, population will be $$2\times x=2x$$
    After $$10$$ years, population will be $$2\times 2x=4x$$
    After $$15$$ years, population will be $$2\times 4x=8x.$$

    Here, initial population is $$x=300$$.
    After $$15$$ years, population will be $$8x=8\times 300=2400$$

    Hence, the population after $$15$$ years is $$2400$$
  • Question 3
    1 / -0
    What is true about deferred annuity ?
    Solution
    Deferred payment annuities typically offer tax-deferred growth at a fixed or variable rate of return, just like regular annuities. Often deferred payment annuities are purchased for under-age children, with the benefit payments postponed until they reach a certain age. Deferred payment annuities can be helpful in retirement planning.
    Option (A) is correct
  • Question 4
    1 / -0
    If a $ $$12,000$$ car loses $$10$$% of its value every year, what is the worth after $$3$$ years?
    Solution
    After $$1^{st}$$ year the value of car is $$12000\left (1- \dfrac{10}{100}\right) = 10800$$
    The value of car after $$2^{nd}$$ year is $$10800\left (1-\dfrac{10}{100}\right) = 9720$$
    The value of car after $$3^{rd}$$ year is $$9720\left (1-\dfrac{10}{100}\right) = 8748$$
  • Question 5
    1 / -0
    What is the compound interest earned at the end of $$3$$ years?
    I. Simple interest earned on that amount at the same rate and for the same period is $$\text{Rs. } 4500$$.
    II. The rate of interest is $$10\%$$ per annum
    III. Compound interest for $$3$$ years is more than the simple interest for that period by $$\text{Rs. } 465$$.
    Solution
    I. gives, S.I. for $$3$$ years $$= \text{Rs. } 4500$$.   ---------(1)
    II. gives, Rate$$ = 10\%$$ per annum    -------------(2)
    III. gives, $$\text{C.I. - S.I.} = \text{Rs. }465$$.
    Clearly, using I and III we get,  $$\text{C.I. } = \text{Rs. } (465 + 4500)$$.
    Thus, II is redundant.

    $$\because$$ Simple interest $$=\dfrac{P \times R \times T}{100}$$
    $$\implies P=\dfrac{ \text{S.I.}\times 100}{R \times T} $$  ----------(3)
    $$\therefore$$ From (1), (2) and (3),  we get $$P= \left (\dfrac {100\times 4500}{10\times 3}\right ) = \text{Rs }15,000$$.
    Now, Amount $$=P \left(1+\dfrac{R}{100}\right)^n$$  where, $$n$$ is the number of years
    $$\implies \text{C.I.}=$$  $$\text{Amount}-P$$
    Thus, III is redundant.
    $$\therefore$$ Either II or III is redundant.
  • Question 6
    1 / -0
    An amount of $$Rs. x$$ at compound interest at $$20$$% per annum for $$3$$ years becomes y. What is $$y : x$$?
    Solution
    $$y = x\left (1 + \dfrac {20}{100}\right )^{3} = x\left (\dfrac {6}{5}\right )^{3}$$
    $$\Rightarrow \dfrac {y}{x} = \dfrac {216}{125}$$
    $$\therefore y : x = 216 : 125$$.
  • Question 7
    1 / -0
    Which of the following is  true about annuity?
    Solution
    $$\Rightarrow$$  The true statement about annuity is $$It\,\,is\,\,sequence\,\,of\,\,equal\,\,instalments.$$
    $$\Rightarrow$$  Series of payments at fixed intervals, guaranteed for a fixed number of years or the lifetime of one or more individuals.
    $$\Rightarrow$$  Annuities are insurance products that provide long-term income through a stream of future payments. 
    $$\Rightarrow$$  While investment annuities save money for retirement and beneficiaries, structured settlement annuities stem from personal-injury legal cases, wrongful-death claims or lottery payouts. When unexpected circumstances arise and require immediate funds, you can sell these payments for a lump sum of cash.
  • Question 8
    1 / -0
    Which of the following comes under Annuity due?

    Solution
    An annuity is a contract aimed at generating steady income during retirement, where in lump sum payment is made by an individual to obtain certain amounts immediately or at some point of future
    all of above comes under annuity.
    It includes Life insurance Premium, Recurring Deposit Payments, Advance Payment of monthly house rent.
  • Question 9
    1 / -0
    The price of commodity $$X$$ increases by $$40$$ paise every year, while the price of commodity $$Y$$ increases by $$15$$ paise every year. If in $$2001$$, the price of commodity $$X$$ was Rs. $$4.20$$ and that of $$Y$$ was Rs. $$6.30$$, in which year commodity $$X$$ will cost $$40$$ paise more than the commodity $$Y$$?
    Solution
    Suppose commodity $$X$$ will cost $$40$$ paise more than $$Y$$ after $$z$$ years.

    Then, $$\left( 4.20+0.40z \right) -\left( 6.30+0.15z \right) =0.40$$

    $$\Rightarrow 0.25z=0.40+2.10$$

    $$\Rightarrow z=\dfrac { 2.50 }{ 0.25 } =\dfrac { 250 }{ 25 } =10$$.

    $$\therefore$$ $$X$$ will cost $$40$$ paise more than $$Y$$ $$10$$ years after $$2001 $$ which is  $$2011$$.
  • Question 10
    1 / -0
    Three types of annuities are
    Solution
    $$\Rightarrow$$  Three types of annuities are : 
    $$(1)$$ $$Annuity\,\, certain$$ - Annuity that, as a minimum, guarantees a fixed number of payments. It continues over the life of the annuitant, even if he or she lives beyond the number of payments specified in the annuity contract. In case the annuitant dies before exhausting the payments, a named beneficiary continues to receive the remaining number. Also called life annuity certain or life annuity certain and continuous.
    $$(2)$$ $$Annuity\,\, contingent$$ - An annuity arrangement in which the beneficiary does not begin receiving payments until a specified event occurs. A contingent annuity may be set up to begin sending payments to a beneficiary upon the death of another individual who wishes to ensure financial stability for the beneficiary, or upon retirement or disablement of the beneficiary.
    $$(3)$$ $$Annuity\,\, perpetual$$ - Annuity derived from an asset (such as an income generating security) where the life span of the annuitant (security holder or his or her beneficiary) is of no consequence.
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