Tag: financial mathematics

Questions Related to financial mathematics

A bank pays interest at the rate of 8 % per annum compounded half yearly. Find how much should be deposited in the bank (approximately) at the beginning of each half year in order to accumulate Rs 8000 for 3 years.

business mathematics and statistics insurance and annuity amount of an annuity annuities financial mathematics

  1. 994

  2. 1161

  3. 4532

  4. 2341

Show answer
Correct Option: B
Explanation:
$A=P(1+\cfrac{r}{100})^n$
$r=8\%/2=4\%, n=2\times 3=6$
$\implies 8000=P[(1+\cfrac{4}{100})^6$$+(1+\cfrac{4}{100})^{5}......$$+(1+\cfrac{4}{100})^{1}]\\ \implies 8000=P\times 21.5718\\ \implies P=Rs.1159\approx Rs.1161$

Find the future value of an ordinary amount of Rs 4000 each six months for 10 years at 8% per annum , compounded semi-annually.

business mathematics and statistics insurance and annuity amount of an annuity annuities financial mathematics

  1. $123877$

  2. $175640$

  3. $213457$

  4. $324156$

Show answer
Correct Option: A
Explanation:

$P=Rs.4000$

Amount payable in half yearly so $,r=8\%/2=4\%,t=10\times 2=20$
$A=\sum _{ n=1 }^{ 20 }{ P{ (1+\cfrac { r }{ 100 } ) }^{ n } } \ =\sum _{ n=1 }^{ 20 }{ 4000{ (1+\cfrac { 4 }{ 100 } ) }^{ n } } \ =4000\times 30.969\ =Rs.123877$

Find the least number of years for which an annuity Rs 1000 must run in order that its amount just exceeds Rs 16000 at 5% pa. compounded annually.

business mathematics and statistics insurance and annuity amount of an annuity annuities financial mathematics

  1. $12$

  2. $9$

  3. $2$

  4. $25$

Show answer
Correct Option: A
Explanation:

$P=4000, r=5\%$

$A=\sum _{ n=1 }^{ n _0 }{ P{ (1+\cfrac { r }{ 100 } ) }^{ n } } \ =\sum _{ n=1 }^{ n _0 }{ 1000{ (1+\cfrac { 5 }{ 100 } ) }^{ n }\  } >1600\ =\sum _{ n=1 }^{ n _0 }{ { (1+\cfrac { 5 }{ 100 } ) }^{ n }\  } >16$
Since it is a sum of a infinite GP. We can write it as a
$\cfrac  {(1.05^{n _0}-1)}{(1.05-1)}\times 1.05>16$
$\implies (1.05)^{n _0}>1.7619$
Taking log on both sides
$\implies \log{(1.05)^{n _0}}>\log 1.7619$
$\implies n _0>\cfrac{\log (1.7619)}{\log (1.05)}$
$\implies n _0>11.6$
$\implies n _0=12$
Hence, least no. of years$=12$.

Find the amount of the annuity of Rs 150 payable in half yearly instalments  for 15 years at 4% per annum interest also payable half yearly

business mathematics and statistics insurance and annuity amount of an annuity annuities financial mathematics

  1. Rs.$9903.45$

  2. Rs.$3003.45$

  3. Rs.$8103.45$

  4. Rs.$3103.45$

Show answer
Correct Option: D
Explanation:

$P=Rs.150$

Amount payable in half yearly so $,r=4\%/2=2\%,t=15\times 2=30$
$A=\cfrac{1}{2}\sum _{ n=1 }^{ 30 }{ P{ (1+\cfrac { r }{ 100 } ) }^{ n } } \ =\cfrac{1}{2}\sum _{ n=1 }^{ 30 }{ 150{ (1+\cfrac { 2 }{ 100 } ) }^{ n } } \ =75\times 41.38\ =Rs.3103.45$

A sum of Rs 2522 is borrowed from a money lender at 5% per annum compounded annually.If this amount is to be paid back in 3 equal instalments , find the annual instalments (approximately).

business mathematics and statistics insurance and annuity amount of an annuity annuities financial mathematics

  1. 925

  2. 800

  3. 875

  4. 567

Show answer
Correct Option: A
Explanation:

$P=\cfrac{A}{(1+\cfrac{R}{100})^n}$

$\implies 2522= \cfrac{A}{(1+\cfrac{5}{100})^1}$$+\cfrac{A}{(1+\cfrac{5}{100})^2}+$$\cfrac{A}{(1+\cfrac{5}{100})^3}$
$ \implies A=926\approx 925$

What is the amount of annuity(approximately) due of Rs 100 yearly payable half yearly for 15 years at 10 % compound interest per annum half yearly.

business mathematics and statistics insurance and annuity amount of an annuity annuities financial mathematics

  1. 3491

  2. 1456

  3. 5434

  4. 2341

Show answer
Correct Option: A
Explanation:

$r=\cfrac{10\%}{2}=5\%,n=2\times 15=30,A=Rs.100$

Amount of annuity due payable half yearly
$=(1/2)\cfrac{A}{r}\times (1+r)\times[(1+r)^n-1]$
$=(1/2)\cfrac{100}{0.05}\times (1+0.05)\times[(1+0.05)^{30}-1]\=Rs.3488\approx  Rs.3491$

Which of the following comes under Annuity due?

business mathematics and statistics insurance and annuity amount of an annuity annuities financial mathematics

  1. Life insurance Premium

  2. Recurring Deposit Payments

  3. Advance Payment of monthly house rent

  4. All of the above

Show answer
Correct Option: D
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.

Suppose you deposit $ \$900$ per month into an account that pays $4.8 \%$ interest, compounded monthly. How much money will you have after $9$ months? 

business mathematics and statistics insurance and annuity amount of an annuity annuities financial mathematics

  1. $ $8432.97$

  2. $ $1372.44$

  3. $ $9812.97$

  4. None of these

Show answer
Correct Option: D
Explanation:

Here, $P=\$900,\,R=4.8\%$ and $T=9$ months $=\dfrac{3}{4}$ year

$\Rightarrow$ $A=P\left (1+\dfrac{R}{100}\right)^{4T}$
$\Rightarrow$ $A=900\times \left (1+\dfrac{4.8}{100}\right)^{4\times \frac{3}{4}}$
$\Rightarrow$ $A=900\times \left (\dfrac{131}{125}\right)^3=900\times 1.1510$
$\Rightarrow$ $A=\$1035.9$

Identify the correct term for the following definition: It is any asset donated to and for the perpetual benefit of a non-profit institution. The donation is usually made with the requirement that the principal remain intact and money earned from investing the principal be used for a specific purpose.

business mathematics and statistics insurance and annuity amount of an annuity annuities financial mathematics

  1. Scholarship fund

  2. Sinking fund

  3. Endowment

  4. None of these

Show answer
Correct Option: C
Explanation:

"It is any asset donated to and fro for the perpetual benefit of a non-profit institution. The donation is usually made with the requirement that the principal remain intact and money earned from investing the principal be used for a specific purpose".

Correct term for he above defination is the Endowment.

Identify the correct term for the following definition: It is a part of a bond indenture or preferred stock charter that requires the issuer to regularly set money aside in a separate custodial account for the exclusive purpose of redeeming the bonds or shares.

business mathematics and statistics insurance and annuity amount of an annuity annuities financial mathematics

  1. Scholarship fund

  2. Sinking fund

  3. Endowment

  4. None of these

Show answer
Correct Option: B
Explanation:

"It is a part of a bond indenture or preferred stock charter that requires the issuer to regularly set money aside in a separate custodial account for the exclusive purpose of redeeming the bonds or shares." The correct term for these definition is $\text{Sinking fund}$.

A sinking fund is an account that is used to deposit and save money to repay a debt or replace a wasting asset in the future. 
In other words, it’s like a savings account that you deposit money in regularly and can only be used for a set purpose.
Private and public corporations often use these funds for bonds.