Installments Part 2

Problem 1: A man borrows RS.2100 and undertakes to pay back with C.I at the rate of 10% in 2 equal yearly installments at the end of 1st and 2nd year. What is the amount of each installment?

Solution:

Formula:C.I=A=\frac{X}{(1+\frac{R}{100})}+\frac{X}{(1+\frac{R}{100})^{2}}+\frac{X}{(1+\frac{R}{100})^{2}}

2100=\frac{X}{(1+\frac{10}{100})}+\frac{X}{(1+\frac{10}{100})^{2}}

2100=\frac{X}{(\frac{110}{100})}+\frac{X}{(\frac{110}{100})^{2}}

2100=X\times \frac{10}{11}+X\times \frac{100}{121}

2100=\frac{110X+100X}{121}=\frac{210X}{121}

2100=\frac{210X}{121}=1210

Shortcut: (1+r%)=>(1+\frac{r}{100})=1+\frac{10}{100}=\frac{11}{10}

I=A\times \frac{Big number}{sum}\times 1+r%

=2100\times \frac{11}{21}\times \frac{11}{10}=1210

 

Problem 2: A=1820  R=20% Time=3 C.I=?

Solution: (1+\frac{r}{100})=1+\frac{20}{100}=\frac{120}{100}=\frac{6}{5}

1:\frac{5}{6}:(\frac{5}{6})^{2}

1:\frac{5}{6}:\frac{25}{36}

36:30:25

I=1820\times \frac{36}{91}\times \frac{6}{5}=216\times 4=864

Problem 3: A man buys a scooter on making a cash draw payment of 16224 and promises to pay two more yearly installment of equivalent amount in the next two years. If the rate of the installment is 4% per annum then the cash value of the scooter is?

Solution:X=A\times (1+\frac{R}{100})

16224=P_{1}(1+\frac{R}{100})

16224=P_{1}(1+\frac{4}{100})

P_{1}=\frac{1622\times 25}{26}=15600

16224=P_{2}(1+\frac{4}{100})^{2}

P_{2}=15000

Total value = 16244+15600+15000 = 46,844

Installments Part 1

Problem 1: What annual installment will discharge a dept of 6450/- due in 4 years at 5% S.I?

Solution: S.I=\frac{100\times A}{100\times Time+\frac{R\times t(T-1)}{2}}

\frac{100\times 6450}{400+\frac{5\times 4\times 3}{2}}=\frac{100\times 6450}{430}=1500

Method:

100 |105 |110|115

430——->6450

100——->?

\frac{6450\times 100}{430}=1500

 

Problem 2: What annual payment will discharge a debt of RS 944 in 4 annual equal installments at the rate of 12% on S.I?

Solution:

100| 112| 124 | 136

472——->944

100———>?

\frac{944\times 100}{472}=200

 

Problem 3: The annual payment of Rs.700 in 5 years at the rate of 10% S.I will discharge a debt of what amount?

Solution:

1st year——>700—->10%\frac{700\times 10}{100}=70

2nd year—–>770+70

3rd year—–>840+70

4th year—–>910+70

5th year——>980

Total amount=4200