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CBSE Questions for Class 11 Commerce Applied Mathematics Basics Of Financial Mathematics Quiz 8 - MCQExams.com
CBSE
Class 11 Commerce Applied Mathematics
Basics Of Financial Mathematics
Quiz 8
What is true about deferred annuity ?
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0%
It is an annuity in which the first payment is postponed for period of times.
0%
It is annuity when payments are made at the end of each payment.
0%
It is annuity when payments are made at the beginning of each payment.
0%
None of the above
Explanation
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
What principal will amount to $$Rs. 1352$$ in $$2$$ years at $$4\%$$ compound interest?
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0%
$$Rs. 1250$$
0%
$$1200$$
0%
$$Rs. 1000$$
0%
$$Rs. 1300$$
Explanation
Given data : $$A = Rs. 1352, r = 4$$ and $$n = 2$$
We know that,
$$A = p\left [1 + \cfrac {r}{100}\right ]^{n}$$
$$1352 = p\left [1 + \cfrac {4}{100}\right ]^{2}$$
$$1352 = p\times \cfrac {26}{25}\times \cfrac {26}{25}$$
$$\Rightarrow P = \text{ Rs. } 1250$$
A merchant commences with a certain capital and gains annually at the rate of $$25$$%. At the end of $$3$$ years he is worth $$Rs. 10,000$$. What was his original capital?
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0%
$$Rs. 2500$$
0%
$$Rs.5120$$
0%
$$Rs. 5000$$
0%
$$Rs. 6200$$
Explanation
Let the original sum of the amount be $$x.$$
Given:
$$A=Rs.\ 10,000$$
$$t=3$$ years
$$r=25\%$$
So, by using the formula to calculate the compound interest,
$$\begin{aligned}{}A& = P{\left( {1 + \frac{r}{{100}}} \right)^t}\\10,000& = P{\left( {1 + \frac{{25}}{{100}}} \right)^3}\\10,000& = P{\left( {1 + \frac{1}{4}} \right)^3}\\10,000 &= P{\left( {\frac{5}{4}} \right)^3}\\P& =Rs.\ 5120\end{aligned}$$
Hence, the initial amount was $$Rs.\ 5120.$$
At what rate per cent compound interest does a sum of money become four fold in $$2$$ years?
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0%
$$25$$%
0%
$$50$$%
0%
$$100$$%
0%
$$10$$%
Explanation
$$4x = x\left (1 + \dfrac {r}{100}\right )^{2}$$
$$\because \left (1 + \dfrac {r}{100}\right )^{2} = 4$$ or $$1 + \dfrac {r}{100} = 2$$
or $$r = 100$$%
Find the compound interest of $$Rs. 800$$ for $$3$$ years at $$5\ p.c.$$
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0%
$$Rs. 920$$
0%
$$Rs. 850$$
0%
$$Rs. 926.10$$
0%
$$Rs. 126.10$$
A sum of money on compound interest amounts to Rs. $$9,680$$ in $$2$$ years and to Rs. $$10,648$$ in $$3$$ years. What is the rate of interest per annum?
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0%
$$5\%$$
0%
$$10\%$$
0%
$$15\%$$
0%
$$20\%$$
Explanation
Given that Rs. $$9,680$$ becomes Rs. $$10,648$$ in one year
therefore, $$ \text{Interest }=$$ Rs. $$10648 -$$ Rs. $$9,680 =$$ Rs, $$968$$
$$\Rightarrow \text{Rate} = \dfrac {\text{Interest} \times 100}{P\times t}$$
$$= \dfrac {968\times 100}{9680 \times 1} = 10\%$$
Thus the rate of interest per annum is $$10\%$$.
Which of the following comes under Annuity due?
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0%
Life insurance Premium
0%
Recurring Deposit Payments
0%
Advance Payment of monthly house rent
0%
All of the above
Explanation
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.
What is the least number of complete years in which a sum of money at $$20\%$$ compound interest will be more than doubled?
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0%
$$7$$
0%
$$6$$
0%
$$5$$
0%
$$4$$
Explanation
Let Principal amount $$ = Rs\,P $$
formula of compound interest,
Amount $$ = P \left ( 1+\dfrac{r}{m} \right )^{mt} $$
Acc. to question,
$$ 2P = P \left ( 1+\dfrac{20}{100} \right )^{t} $$
$$ \Rightarrow 2 = (1.2)^{t} $$
$$ \Rightarrow \boxed{t = 4} $$
Aman gave Rs.$$9500$$ as a loan to Megh at the rate of $$4\%$$ p.a. compounded yearly. Megh returned the amount after two years. Calculate the interest on the first year's interest.
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0%
$$380$$
0%
$$270$$
0%
$$15.2$$
0%
$$40$$
Explanation
$$P=9500,R=4,T=2$$ years
Interest in $$1$$ year$$=\cfrac { P\times R\times 1 }{ 100 } $$
$$=\cfrac { 9500\times 4 }{ 100 } $$
$$=380$$
Interest on interest$$=\cfrac { 380\times 4\times 1 }{ 100 } $$
$$=15.2$$
What is true about deferred annuity ?
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0%
It is an annuity when the payments are made at the end of payment period.
0%
It is an annuity when the payments are made at the beginning of payment period.
0%
It is an annuity when the payments are made at the middle of payment period.
0%
None of the above
Explanation
$$\Rightarrow$$ True statement about deferred annuity is,
$$-\,It\,is\,an\,annuity\,when\,the\,payment\,are\,made\,at\,the\,end\,of\,payment\,period.$$
$$\Rightarrow$$ A deferred annuity is an insurance contract designed for long-term savings.
$$\Rightarrow$$ Unlike an immediate annuity, which starts annual or monthly payments almost immediately, investors can delay payments from a deferred annuity indefinitely. During that time, any earnings in the account are tax-deferred.
A sum of money put out at compound interest amount in two years to $$Rs. 2809$$, and in three years to $$Rs. 2977.54$$. Find the rate per cent
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0%
$$6$$%
0%
$$10$$%
0%
$$4$$%
0%
$$3$$%
Explanation
Difference in amounts $$= 2977.54-2809 = Rs. 168.54$$
$$Rs.168.54$$ is the interest on $$Rs. 2809$$ in one year
$$Rate=\dfrac{\text{Difference in amounts}}{\text{Initial amount}}\times 100$$
$$Rate=\dfrac{168.54}{2809} \times 100$$
$$Rate= 6\%$$ (The rate is per annum)
The first year's interest on a sum of money lent at $$8$$% compound interest is $$Rs. 48$$. The second year's amount is
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0%
$$Rs. 48$$
0%
$$Rs. 51.48$$
0%
$$Rs. 56.48$$
0%
$$Rs. 96$$
A sum of money placed at compound interest doubles itself in $$4$$ years. In how many years will it amount to eight times itself?
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0%
$$16$$
0%
$$8$$
0%
$$12$$
0%
$$20$$
The compound interest on a certain sum for $$2$$ years is $$Rs. 40.80$$ and the simple interest is $$Rs. 40$$. Find the rate p.c.?
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0%
$$Rs. 4$$
0%
$$4$$%
0%
$$Rs. 0.80$$
0%
$$8$$%
The calculation of interest on the interest of principal amount is called
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0%
simple interest
0%
compound interest
0%
multiple interest
0%
interest quarterly compounded
Explanation
The calculation of interest on the interest of principal amount is called $$Compound\,\,interest$$.
Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest.
It is the result of reinvesting interest, rather than paying it out, so that interest in the next period is then earned on the principal sum plus previously accumulated interest.
Compound interest is standard in finance and economics.
Anagha borrowed Rs.$$ 70,000$$ from her friend at the rate of $$3.5\%$$ p.a.compounded yearly. She returned the amount after three years. So calculate interest of first year and second year .
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0%
$$Rs.2,450, 85.75$$
0%
$$Rs.2,450, 2,450$$
0%
$$Rs.2,450, 2,535.75$$
0%
$$Rs.2,450, 2100$$
Explanation
$$P=70000,R=3.5$$%
Interest in $$1$$st year$$=\cfrac { P\times R\times T }{ 100 } $$
$$=\cfrac { 70000\times 3.5\times 1 }{ 100 } $$
$$=2450$$
Now, $$(2450+P)$$ will be principal amount for $$2$$nd year since interest is compounded yearly
Interest in $$2$$nd year$$=\cfrac { { P }^{ ' }\times R\times T }{ 100 } $$
$$=\cfrac { (2450+70000)\times 3.5\times 1 }{ 100 } $$
$$=724.5\times 3.5=2535.75$$
Megha lended Rs.$$8000$$ as a loan for $$4$$ years at the rate $$4\%$$ compounded annualy. Calculate the interest she will recive by the method of simple interest.
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0%
$$8963.26$$
0%
$$9358.86$$
0%
$$1358.86$$
0%
$$9863.25$$
Explanation
$$P=8000,R=4$$%, $$T=4$$
Interest in $$1$$st year$$=\cfrac { P\times R\times T }{ 100 } $$
$$=\cfrac { 8000\times 4\times 1 }{ 100 } $$
$$=320$$
Now, Principal amount will be $$(P+320)$$ since the interest in compounded annually.
Interest in $$2$$nd year$$=\cfrac { { P }^{ ' }\times R\times T }{ 100 } $$
$$=\cfrac { 8320\times 4\times 1 }{ 100 } $$
$$=332.8$$
Now, $$P''=332.8+P'$$
Interest in $$3$$rd year$$=\cfrac { 8652.8\times 4\times 1 }{ 100 } =346.112$$
Interest in $$4$$th year$$=\cfrac { (346.112+8652.8)\times 4\times 1 }{ 100 } =359.956$$
Total interest$$=320+332.8+346.112+359.95$$
$$=1358.86$$
The bank offers senior citizens intrest at the rate $$9\%$$ p.a compounded yearly on a fixed deposit. What interest will be received at the end of $$5$$ years if Rs.$$10,000$$ are deposited. Calculate by the method of simple interest.
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0%
$$5386.23$$
0%
$$5500.23$$
0%
$$6523.65$$
0%
$$4367.78$$
Explanation
$$P=10000,R=9,T=5$$ yrs
Interest in $$1$$st year$$=\cfrac { P\times R\times T }{ 100 } $$
$$=\cfrac { 10000\times 9\times 1 }{ 100 } $$
$$=900$$
$$P'=(900+10000)$$
Interest in $$2$$nd year$$=\cfrac { 10900\times 9\times 1 }{ 100 } =981$$
Interest in $$3$$rd year$$=\cfrac { 11881\times 9\times 1 }{ 100 }$$
$$=1069.29$$
Interest in $$4$$th year$$=\cfrac { 12950.29\times 9\times 1 }{ 100 }$$
$$=1165.5261$$
Interest in $$5$$th year$$=\cfrac { 14115.81\times 9\times 1 }{ 100 }$$
$$=1270.42$$
Total interest$$=900+981+1069.29+1165.52+1270.42$$
$$=5386.23$$
A businessman borrowed the Rs.$$45$$ lakh for two years at the rate $$2.5\%$$ p.a. compounded annually. Calculate the compound interest by simple interest method.
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0%
$$2,23000$$
0%
$$2,27,812.5$$
0%
$$5,65,563$$
0%
$$2,00,000$$
Explanation
$$\Rightarrow$$ Here, Principal amount for first year is $$Rs.45,00,000$$ and $$R=2.5\%$$.
$$\Rightarrow$$ Interest for first year = $$\dfrac{4500000\times 2.5}{100}=Rs.1,12,500$$
$$\Rightarrow$$ Principal amount for second year = $$Rs.4500000+Rs.112500=Rs.46,12,500$$
$$\Rightarrow$$ Second year interest = $$\dfrac{4612500\times 2.5}{100}=Rs.1,15,312.5$$
$$\Rightarrow$$ Total interest for 2 yeras = $$Rs.1,12,500+Rs.1,15,312.5=Rs.2,27,812.5$$
Amar gave Rs.$$50,000 $$ as a loan to Amir at the rate of $$4\%$$ p.a. Amir return the amount after two years. Calculate the interest on the first year's interest.
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0%
$$200$$
0%
$$70$$
0%
$$80$$
0%
$$60$$
Explanation
$$1$$ year interest$$=\cfrac { P\times R\times T }{ 100 } $$
$$=\cfrac { 50000\times 4\times 1 }{ 100 } =2000$$
Interest of $$1$$ year interest$$=\cfrac { \left( { P }^{ ' }\times R\times T \right) }{ 100 } $$
$$=\cfrac { 2000\times 4\times 1 }{ 100 } $$
$$=80$$
An industrialist borrowed the $$Rs\ 75,000$$ for two years at the rate $$2.5\%$$ p.a.compounded annually. Calculate the total amount compound interest by simple interest method.
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0%
$$2750$$
0%
$$3750$$
0%
$$78,795$$
0%
$$78,796.87$$
Explanation
$$P=75000,R=2.5$$%, Time$$=2$$yrs
Interest in $$1$$st year$$=\cfrac { P\times R\times T }{ 100 } $$
$$=\cfrac { 75000\times 2.5\times 1 }{ 100 } $$
$$=1875$$
$$P'=(1875+P)$$
Interest in $$2$$nd year$$=\cfrac { { P }^{ ' }\times R\times T }{ 100 } $$
$$=\cfrac { 76875\times 2.5\times 1 }{ 100 } $$
$$=1921.875$$
Total interest$$=1875+1921.875$$
$$=3796.875$$
Total amount=Principal$$+$$Total interest
$$=75000+3796.875$$
$$=78796.875$$
Depreciation is the process of valuation of asset.
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0%
True
0%
False
Explanation
Depreciation means fall in the value of assets. The net result of an asset's depreciation is that sooner or later the asset will become useless. Depreciation is the process of reduction in the value of asset.
What principal will amount to Rs. $$9,744$$ in two years, if the rates of interest for successive years are $$16$$% and $$20$$% respectively?
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0%
$$7000$$
0%
$$8000$$
0%
$$5000$$
0%
$$9000$$
Explanation
$$\Rightarrow$$ Let the principal (P) be $$Rs.x$$.
$$\Rightarrow$$ Rate of interests for two successive years are $$(R_1)\,\,16\%$$ and $$(R_2)\,\,20\%$$.
$$\Rightarrow$$ $$A=P(1+\dfrac{R_1}{100})(1+\dfrac{R_2}{100})$$
$$\Rightarrow$$ $$9744=x(1+\dfrac{16}{100})(1+\dfrac{20}{100})$$
$$\Rightarrow$$ $$9744=x\times \dfrac{29}{25}\times {6}{5}$$
$$\Rightarrow$$ $$9744=\dfrac{174}{125}x$$
$$\therefore$$ $$x=\dfrac{9744\times 125}{174}$$
$$=56\times 125=Rs.7000$$
$$\therefore$$ Hence, principal = $$Rs.7000$$.
A sum of Rs.$$8,000$$ is invested for $$1$$ years at $$10$$ % per annum compound interest. Calculate :interest for the second year.
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0%
$$880$$
0%
$$860$$
0%
$$800$$
0%
$$1000$$
Explanation
$$\Rightarrow$$ Here we have, $$P=Rs.8000,\, T=1$$ and $$R=10\%$$
$$\Rightarrow$$ $$I=\dfrac{P\times R\times T}{100}$$
$$\Rightarrow$$ $$I=\dfrac{8000\times 10\times 1}{100}$$
$$\Rightarrow$$ $$I=Rs.800$$
$$\therefore$$ Interest for first year is $$Rs.800$$.
$$\Rightarrow$$ Interest for second year = $$800+\dfrac{10}{100}\times 800=800+80=Rs.880$$
Calculate compound interest for Rs $$15,000$$ for $$1$$ year at $$16$$% compounded semi -annually.
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0%
Rs.$$3172$$
0%
Rs.$$2496$$
0%
Rs.$$3000$$
0%
Rs.$$2572$$
Explanation
Given:
$$\Rightarrow$$ $$P=$$ Rs.$$15000,\,T=1\ year=2$$ and $$R=16\%$$
$$R_{eq}=8\%$$ Since, semi-annually compounded.
$$T_{eq}=2.T= 2.$$ Since, semi-annually compounded.
$$\Rightarrow$$ $$A=P(1+\dfrac{R_{eq}}{100})^{T_{eq}}$$
$$\Rightarrow$$ $$A=15000\times (1+\dfrac{8}{100})^2$$
$$\Rightarrow$$ $$A=15000\times (\dfrac{27}{25})^2$$
$$\Rightarrow$$ $$A=15000\times (\dfrac{729}{625})$$
$$\therefore$$ $$A=$$Rs.$$17496$$
$$\therefore$$ $$C.I.=A-P=$$Rs. $$17496- $$Rs.$$15000=$$Rs.$$2496.$$
Ranjana borrowed the money Rs$$1,00,000$$ for $$3$$ years at the rate $$3.5\%$$ p.a. compounded annually. Calculate interest to be paid.
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0%
$$10871.78$$
0%
$$1000.8$$
0%
$$8710.68$$
0%
$$245$$
Explanation
$$\Rightarrow$$ Here, Principal amount for first year = $$Rs.1,00,000$$
$$\Rightarrow$$ First year Interest = $$\dfrac{100000\times 3.5}{100}=Rs.3500$$
$$\Rightarrow$$ Principal amount for second year = $$Rs.1,00,000+Rs.3500=Rs.1,03,500.$$
$$\Rightarrow$$ Second year interest = $$\dfrac{103500\times 3.5}{100}=Rs.3622.5$$
$$\Rightarrow$$ Principal amount for third year = $$Rs.1,03,500+Rs.3622.5=Rs.1,07,122.5$$
$$\Rightarrow$$ Third year interest = $$\dfrac{107122.5\times 3.5}{100}=Rs.3749.28$$
$$\therefore$$ Total Interest = $$Rs.3500+Rs.3622.5+Rs.3749.28=Rs.10871.78$$
A man lends Rs. $$12,500$$ at $$12$$% for the first year, at $$15$$% for the second year and at $$18$$% for the third year. If the rates of interest are compounded yearly; find the difference between the C.I. for the first year and the compound interest for the third year.
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0%
$$\text{Rs }1,498$$
0%
$$\text{Rs }1,598$$
0%
$$\text{Rs }1,298$$
0%
$$\text{Rs }1,398$$
A bank pays interest at the rate of $$8\%$$ per annum compounded yearly. Find the interest by simple interest method if $$Rs.\ 8000$$ was deposited for $$3$$ years.
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0%
$$Rs.\ 1000$$
0%
$$Rs.\ 2077.7$$
0%
$$Rs.\ 2000$$
0%
$$Rs.\ 3456$$
Explanation
$$P=Rs.\ 8000,R=8$$%, Time period$$=3$$ years
Interest in $$1$$st year $$=\cfrac { P\times R\times T }{ 100 } $$
$$=\cfrac { 8000\times 8\times 1 }{ 100 } $$
$$=Rs.\ 640$$
Principal amount for $$2$$nd year will be,
$$P'=P+640$$
$$=Rs.\ 8000+Rs.\ 640$$
$$=Rs.\ 8640$$
Interest in $$2$$nd year$$=\cfrac { 8640\times 8 }{ 100 } $$
$$=Rs.\ 691.2$$
Principal amount for $$2$$nd year will be,
$$P''=P'+691.2$$
$$=Rs.\ 8640+Rs.\ 691.2$$
$$=Rs.\ 9331.2$$
Interest in $$3$$rd year $$=\cfrac { 9331.2\times 8 }{ 100 } $$
$$=Rs.\ 746.5$$
So, total interest $$=640+691.2+746.5$$
$$=Rs.\ 2077.69$$
$$\approx Rs.\ 2077.7$$
The population of a town $$3$$ years ago was Rs. $$50,000$$.If the population in these three years has increased at the rate of $$10\%,15\%$$ and $$8\%$$ respectively, find the present population.
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0%
Rs. $$68,210$$
0%
Rs. $$68,310$$
0%
Rs. $$68,410$$
0%
Rs. $$68,510$$
Explanation
Let $$P=.50,000$$ and
$$R_1=10\%,\\ R_2=15\%,\\ R_3=8\%$$.
Present population = $$P\times \left (1+\dfrac{R_1}{100}\right)\left (1+\dfrac{R_2}{100}\right)\left (1+\dfrac{R_3}{100}\right)$$
On substituiting the given values,
Present population $$=$$ $$50000\times \left (1+\dfrac{10}{100}\right)\times \left (1+\dfrac{15}{100}\right)\times \left (1+\dfrac{8}{100}\right)$$
$$=$$ $$50000\times \dfrac{11}{10}\times \dfrac {23}{20}\times \dfrac{27}{25} =68310$$
Therefore, p
resent population $$=$$ $$68310$$.
If $$600$$ dollars is deposited in a bank account for $$4$$ years at $$8$$% per annum . Calculate interest using compound interest formula.
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0%
$$216$$
0%
$$216.3$$
0%
$$220.6$$
0%
$$224.8$$
Explanation
Amount at the end of $$4$$ years
$$=600(1+0.08)^4$$
$$ =816.29$$
Compound interest $$=816.29-600=216.29 $$
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