My Math Forum annuity

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 May 19th, 2014, 01:21 AM #1 Newbie   Joined: May 2014 From: pakistan Posts: 3 Thanks: 0 annuity i have a qs regarding annuity? a bank offers a car loan for car above Rs.3000000 tax free.a man likes a car worth 110% more than the lower limit.he keep some of the money in the bank and lease the car from the bank using the left over money.he keeps 70% in the bank,gives the car initial payment with the rest and takes the out.the bank gives an interest of 8% on the deposited money.to lease the car he has two options,he can get a simple interest of 6% per month over 2 years or a compound interest of 3% per month over 4 years.the car he bought was tax by the government at 15%, had to pay to the bank. if he originally had 7000000 to begin with,which scheme is better assuming that he has other sources of income and the bank decides to distribute the total loan and interest equally each month.give answer in terms of annuity? if the inflation rate runs at 7% per annum,considering the future rice of car and the laon scheme man opted for,now was getting a car on lease a wise option?
May 19th, 2014, 01:27 PM   #2
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Quote:
 Originally Posted by fatim i have a qs regarding annuity? a bank offers a car loan for car above Rs.3000000 tax free.a man likes a car worth 110% more than the lower limit.he keep some of the money in the bank and lease the car from the bank using the left over money.he keeps 70% in the bank,gives the car initial payment with the rest and takes the out.the bank gives an interest of 8% on the deposited money.to lease the car he has two options,he can get a simple interest of 6% per month over 2 years or a compound interest of 3% per month over 4 years.the car he bought was tax by the government at 15%, had to pay to the bank. if he originally had 7000000 to begin with,which scheme is better assuming that he has other sources of income and the bank decides to distribute the total loan and interest equally each month.give answer in terms of annuity? if the inflation rate runs at 7% per annum,considering the future rice of car and the laon scheme man opted for,now was getting a car on lease a wise option?
Can you repost; get someone to clarify your English;
clarify the compounding frequencies of rates:
3% per month means what? 7% per annum means what?
Thank you.

 May 19th, 2014, 11:38 PM #3 Newbie   Joined: May 2014 From: pakistan Posts: 3 Thanks: 0 3% per month over 4 year is the compound interest and inflation rate is 7% per anum. 3% per month means (3/12)%=0.25%
May 20th, 2014, 01:45 PM   #4
Math Team

Joined: Oct 2011

Posts: 14,597
Thanks: 1038

Quote:
 Originally Posted by fatim i have a qs regarding annuity? a bank offers a car loan for car above Rs.3000000 tax free.a man likes a car worth 110% more than the lower limit.he keep some of the money in the bank and lease the car from the bank using the left over money.he keeps 70% in the bank,gives the car initial payment with the rest and takes the out.the bank gives an interest of 8% on the deposited money.to lease the car he has two options,he can get a simple interest of 6% per month over 2 years or a compound interest of 3% per month over 4 years.the car he bought was tax by the government at 15%, had to pay to the bank. if he originally had 7000000 to begin with,which scheme is better assuming that he has other sources of income and the bank decides to distribute the total loan and interest equally each month.give answer in terms of annuity? if the inflation rate runs at 7% per annum,considering the future rice of car and the laon scheme man opted for,now was getting a car on lease a wise option?
Maybe someone else will be able to help you; I can't as I don't understand
Strange things are in the problem: like bank pays 8% on savings, and
charges only 6% on loans...wish that bank would move over here...

Good luck...

 November 20th, 2014, 08:34 PM #5 Newbie   Joined: Nov 2014 From: fsd Posts: 1 Thanks: 0 Hello, I need your help.. Thank you Present values amounts are equal of 2 infinite series. The payments are "end of period annuites". First serie: the payments are 100 USD for the first 2 years, for the the following two years are 200 USD, for the following 2 years are 300 USD, and it continues like this to infinity. Second serie : the payments are P for the first 3 years,for the the following three years are 2P, for the following threeyears are 3P, and it continues like this to infinity. what is the value of P?
November 30th, 2014, 05:34 AM   #6
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From: Rawalpindi, Punjab

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Quote:
 Originally Posted by hasseb432 Hello, I need your help.. Thank you Present values amounts are equal of 2 infinite series. The payments are "end of period annuites". First serie: the payments are 100 USD for the first 2 years, for the the following two years are 200 USD, for the following 2 years are 300 USD, and it continues like this to infinity. Second serie : the payments are P for the first 3 years,for the the following three years are 2P, for the following threeyears are 3P, and it continues like this to infinity. what is the value of P?
1st Pereptuity

Code:
100 100 200 200 300 300 ....
2nd Perpetuity

Code:
P P P 2P 2P 2P 3P 3P 3P ....
PV of 1st Perpetuity

Code:
i=10%
c=1
p=2
R=100
Q=100

PV = PV_1 + PV_2

aey(i,c) = (1+i/c)^(1/c)-1
aey(10%,1) = (1+10%/1)^(1/1)-1
aey(10%,1) = (1+10%)^(1)-1
aey(10%,1) = (1.1)^(1)-1
aey(10%,1) = 1.1-1

aey(10%,1) = 0.1

x = (1+aey(i,c))^p
x = (1+10%)^2
x = (1.1)^2
x = 1.21

PV_1 = x^0.5{R/[x-1] + Q/[x-1]^2}
PV_1 = 1.21^0.5{100/[1.21-1] + 100/[1.21-1]^2}
PV_1 = 1.1{100/[0.21] + 100/[0.21]^2}
PV_1 = 1.1{100/[0.21] + 100/[0.0441]}
PV_1 = 1.1{476.19047619047619047619047619048 + 2267.5736961451247165532879818594}
PV_1 = 1.1{3219.9546485260770975056689342404}
PV_1 = 3541.9501133786848072562358276644

PV_1 = R/[x-1] + Q/[x-1]^2
PV_1 = 100/[1.21-1] + 100/[1.21-1]^2
PV_1 = 100/[0.21] + 100/[0.21]^2
PV_1 = 100/[0.21] + 100/[0.0441]
PV_1 = 476.19047619047619047619047619048 + 2267.5736961451247165532879818594
PV_1 = 3219.9546485260770975056689342404

PV = 3541.9501133786848072562358276644 + 3219.9546485260770975056689342404
PV = 6761.9047619047619047619047619048
PV of 2nd perpetuity

Code:
i=10%
c=1
p=3
R=P
Q=P
PV=6761.9047619047619047619047619048

PV = PV_1 + PV_2 + PV_3

aey(i,c) = (1+i/c)^(1/c)-1
aey(10%,1) = (1+10%/1)^(1/1)-1
aey(10%,1) = (1+10%)^(1)-1
aey(10%,1) = (1.1)^(1)-1
aey(10%,1) = 1.1-1

aey(10%,1) = 0.1

x = (1+aey(i,c))^p
x = (1+10%)^3
x = (1.1)^3
x = 1.331

PV_1 = x^(2/3){R/[x-1] + Q/[x-1]^2}
PV_1 = 1.331^0.6667{P/[1.331-1] + P/[1.331-1]^2}
PV_1 = 1.21P{1/[0.331] + 1/[0.331]^2}
PV_1 = 1.21P{1/0.331 + 1/0.109561}
PV_1 = 1.21P{3.0211480362537764350453172205438 + 9.1273354569600496527048858626701}
PV_1 = 1.21P{12.148483493213826087750203083214}
PV_1 = 14.699665026788729566177745730689P

PV_2 = x^(1/3){R/[x-1] + Q/[x-1]^2}
PV_2 = 1.331^0.3333{P/[1.331-1] + P/[1.331-1]^2}
PV_2 = 1.1P{1/[0.331] + 1/[0.331]^2}
PV_2 = 1.1P{1/0.331 + 1/0.109561}
PV_2 = 1.1P{3.0211480362537764350453172205438 + 9.1273354569600496527048858626701}
PV_2 = 1.1P{12.148483493213826087750203083214}
PV_2 = 13.363331842535208696525223391535P

PV_3 = R/[x-1] + Q/[x-1]^2
PV_3 = P/[1.331-1] + P/[1.331-1]^2
PV_3 = P{1/[0.331] + 1/[0.331]^2}
PV_3 = P{1/0.331 + 1/0.109561}
PV_3 = P{3.0211480362537764350453172205438 + 9.1273354569600496527048858626701}
PV_3 = 12.148483493213826087750203083214P

PV = PV1 + PV2 + PV3

6761.9047619047619047619047619048 = 14.699665026788729566177745730689P + 13.363331842535208696525223391535P + 12.148483493213826087750203083214P
6761.9047619047619047619047619048 = 40.211480362537764350453172205438P
6761.9047619047619047619047619048/40.211480362537764350453172205438 = P

P = 168.15856319988551393510071196022
Code:
P = 168.16

 November 30th, 2014, 07:20 PM #7 Member     Joined: May 2014 From: Rawalpindi, Punjab Posts: 69 Thanks: 5 I had made a totaling error in finding present value of 1st perpetuity that led to an incorrect value for P At 10% interest rate both perpetuities A and B have a present value of 5761.9047619047619047619047619039 and the P comes out to 143.29 Code: 5761.9047619047619047619047619039/40.211480362537764350453172205438 = P P = 143.29004329004329004329004329005 The correct PV calculations for 1st perpetuity Code: i=10% c=1 p=2 R=100 Q=100 PV = PV_1 + PV_2 aey(i,c) = (1+i/c)^(1/c)-1 aey(10%,1) = (1+10%/1)^(1/1)-1 aey(10%,1) = (1+10%)^(1)-1 aey(10%,1) = (1.1)^(1)-1 aey(10%,1) = 1.1-1 aey(10%,1) = 0.1 x = (1+aey(i,c))^p x = (1+10%)^2 x = (1.1)^2 x = 1.21 PV_1 = x^0.5{R/[x-1] + Q/[x-1]^2} PV_1 = 1.21^0.5{100/[1.21-1] + 100/[1.21-1]^2} PV_1 = 1.1{100/[0.21] + 100/[0.21]^2} PV_1 = 1.1{100/[0.21] + 100/[0.0441]} PV_1 = 1.1{476.19047619047619047619047619048 + 2267.5736961451247165532879818594} PV_1 = 1.1{2743.7641723356009070294784580499} PV_1 = 3018.1405895691609977324263038549 PV_2 = R/[x-1] + Q/[x-1]^2 PV_2 = 100/[1.21-1] + 100/[1.21-1]^2 PV_2 = 100/[0.21] + 100/[0.21]^2 PV_2 = 100/[0.21] + 100/[0.0441] PV_2 = 476.19047619047619047619047619048 + 2267.5736961451247165532879818594 PV_2 = 2743.7641723356009070294784580499 PV = 3018.1405895691609977324263038549 + 2743.7641723356009070294784580499 PV = 5761.9047619047619047619047619039

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