Compound Interest Part 9

Problem 1: When a certain principal is invested at 16.66% compound interest instead of 12.5% per annum for 2 years the interest is 550 more. Find the principal?

Solution:

12.5% ——–>$\frac{1}{8}$——–>64

16.66%——–>$\frac{1}{6}$——–>36

LCM Of 64 and 36 is 576 is principal

72+72+9=153                                             96+96+16=208

208-153=55

55———->550

576——–>?

$\frac{550\times&space;576}{55}=5760$

Problem 2: Raju took Rs.38400 from Rama at 10% rate of SI and give it to Surya who gives 12.5% rate of C.I compounded annually. If Raju gives the money to Surya for 3 years and returns to Rama immediately. Find the profit of Raju?

Solution:

S.I=$\frac{PTR}{100}=\frac{38400\times&space;10\times&space;3}{100}=11520$

4800*3=14400

600*3=1800

14400+1800+75=16275

16275-11520=4755

Problem 3: A man invested a sum of money in scheme A, at the rate of 15% per annum for S.I, at the end of two years the amount received by him is invested in scheme B at 20% per annum for C.I. If the interest received by him from scheme B at the end of the second year is RS. 2860, then find the sum invested by a man in the beginning?

Solution:

Scheme B=20% C.I

20+20+$\frac{20\times&space;20}{100}=44$%

Scheme A=15% S.I

Assume principal is 100

$S.I=\frac{PTR}{100}=\frac{100\times&space;2\times&space;15}{100}=130$%

44%——–>2860

100%——–>?

$\frac{2860\times&space;100}{44}=6500$

$\frac{6500\times&space;100}{130}=50,000$

Problem 4: A and B have an amount in 2:3 if A buy a car from his money whose price is depreciated by 10% whereas B invested that money in the bank which gives C.I at the rate of 20% per annum. Find the total percentage change in the total amount?

Solution:

10%=$\frac{1}{10}$–  ——>  Depreciates —–>  $\frac{9}{10}$

20%=$\frac{1}{5}$    ———> Increases  ——-> $\frac{6}{5}$

A             :                B

2              :                3

$2\times&space;\frac{9}{10}$    :        $3\times&space;\frac{6}{5}$

1              :            2

$\frac{1}{1}\times&space;100=100$% change

Compound Interest Part 8

Problem 1: An equal principal was invested in two banks first offering 15% simple interest and the second offering compound interest of 20% if the difference of interest from both banks after 3 years was Rs.417. Find the principal invested in each bank?

Solution:

Simple Interest=15*3=45%

Compound Interest=20+20+$\frac{20\times&space;20}{100}$=44%

44+20+$\frac{44\times&space;20}{100}$=72.8%

72.8-45=27.8%

27.8%——–>417

100%———->?

$\frac{417\times&space;100}{27.8}=1500$

Problem 2: Simple interest on a principal of 2 years is 108.80 and compound interest on same principal for the same time period and rate of interest is  RS 115.60. Find the rate of interest?

Solution: Simple interest on a principal of 2 years is 108.80

Note: Simple interest is same for every year

$\frac{108.80}{2}=54.40$

54.40 S.I for the first year

54.40 S.I for the second year

Compound interest on same principal for the same time period and rate of interest is  Rs.115.60

115.60-108.80=6.8

1st year C.I is 54.40

2nd year C.I is 54.40+6.8

54.40|  54.40|  6.8

54.40$\times&space;\frac{x}{100}=6.8$

$x=&space;\frac{6.8\times&space;100}{54.40}=12.5$%

Problem 3: A sum of Rs.2592 was invested in two banks the first bank offers C.I of $16\frac{2}{3}$% compounded annually whereas the second bank offers S.I of $12\frac{1}{2}$%. Find the difference between S.I and C.I of 2 years 6 months?

Solution:

C.I is $16\frac{2}{3}$%=$\frac{1}{6}$

S.I is $12\frac{1}{2}$%=$\frac{1}{8}$

S.I=2592$\times&space;\frac{1}{8}\times&space;\frac{5}{2}=810$

C.I== 432+432+216+72+36+36+6 = 1230

Difference between C.I and S.I = C.I – S.I = 1230-810=420

Compound Interest Part 7

Compounded half-yearly, then rate=$\frac{r}{2}$% and time=2*time

Compounded quarterly, then rate=$\frac{r}{4}$% and time=4*time

Problem1: The compound interest earned on a sum in 3 years at 15% per annum compounded annually is RS.25002. Find the sum?

Solution: R=15%  Time=3 year C.I=25002

1200*3=3600

180*3=540

3600+540+27=4167

4167——>25002

8000——–>?

$\frac{25002\times&space;8000}{6}=48000$ is principle

Problem 2: A sum of RS.19600 is invested at 20% rate of compound interest for 2 years compounded half yearly. then the end of two years compound interest will be how much more than the S.I?

Solution:

Rate=$\frac{20}{2}=10$%  time =2*2=4 years

we will split 4 years into 2 and 2 years

R=10% T=2 years

C.I=10+10+$\frac{10\times&space;10}{100}=21$%

R=21% T=2 years

21+21+$\frac{21\times&space;21}{100}=21+21+4.41=46.41$%

C.I=46.41%

S.I=10*4=40%

46.41-40=6.41%

100%———>19600

6.41%———->?

$\frac{19600\times&space;6.41}{100}=1256.36$

Problem 3: If a sum of Rs.3600 is invested in two different banks for 2 years first offering 20% compound interest compounded annually and second offer 20% compounded half yearly then find the difference of the interest after 2 years?

Solution:

first offering 20% compound interest compounded annually

20%———-C.I———-Annually

20+20+$\frac{20\times&space;20}{100}$ = 44%

second offer 20% compounded half yearly

Rate=$\frac{20}{2}=10$%  , Time=2*2=4 years

10+10+$\frac{10\times&space;10}{100}$=21%

21+21+$\frac{21\times&space;21}{100}$=46.41%

46.41 – 44=2.41%

100%———->3600

2.41%———>?

$\frac{3600\times&space;2.41}{100}$=86.76

Compound Interest Part 6

Problem 1: P=21600, R=$16\tfrac{2}{3}$%, T=3yers, C.I=?

Solution:

Fraction for $16\tfrac{2}{3}$% is $\frac{1}{6}$

36+36+36+6+6+6+1=127

216———–>21600

127———–>?

$\frac{21600\times&space;127}{216}=12700$ is principle.

Problem 2: P=?, R=15%, T=3years, C.I-S.I=1701

Solution:

Fraction for 15% is $\frac{3}{20}$

20*20*20=8000

180+180+180+27=567

567————->1701

8000————->?

$\frac{1701\times&space;8000}{567}=24000$

Problem 3: P=?, T=3 years, 3rd-year C.I-2nd year C.I=420,R=$16\tfrac{2}{3}$%

Solution:

Fraction for $16\tfrac{2}{3}$% is $\frac{1}{6}$

7——->420

216——>?

$\frac{420\times&space;216}{7}=12960$ is principle

Compound Interest Part 5

Problem 1: P=?, R=20%, T=1 year 73 days, C.I=1240

Solution:

Fraction for 20%=$\frac{1}{5}$

$\frac{6}{365}\times&space;73=1.2$

5+1.2 =6.2 is C.I

6.2———–>1240

25————->?

$\frac{1240\times&space;25}{6.2}=5000$ is principle.

Problem 2: P=?,R=$12\tfrac{1}{2}$%, T=1 year 4 months, C.I=1782

Solution:

Fraction for $12\tfrac{1}{2}$% is $\frac{1}{8}$

8+1=9

$\frac{9}{12}\times&space;4=3$

8+3=11

11———->1782

64————>?

$\frac{1782\times&space;64}{11}=10468$ is principal.