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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  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038  Quote:
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 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038  Quote:
what you're saying or asking. 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  
Member Joined: May 2014 From: Rawalpindi, Punjab Posts: 69 Thanks: 5  Quote:
Code: 100 100 200 200 300 300 .... Code: P P P 2P 2P 2P 3P 3P 3P .... 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) = 1.11 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/[x1] + Q/[x1]^2} PV_1 = 1.21^0.5{100/[1.211] + 100/[1.211]^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/[x1] + Q/[x1]^2 PV_1 = 100/[1.211] + 100/[1.211]^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 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) = 1.11 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/[x1] + Q/[x1]^2} PV_1 = 1.331^0.6667{P/[1.3311] + P/[1.3311]^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/[x1] + Q/[x1]^2} PV_2 = 1.331^0.3333{P/[1.3311] + P/[1.3311]^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/[x1] + Q/[x1]^2 PV_3 = P/[1.3311] + P/[1.3311]^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 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) = 1.11 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/[x1] + Q/[x1]^2} PV_1 = 1.21^0.5{100/[1.211] + 100/[1.211]^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/[x1] + Q/[x1]^2 PV_2 = 100/[1.211] + 100/[1.211]^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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