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 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 10\times 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 20}{100}=44%

Scheme A=15% S.I

Assume principal is 100

S.I=\frac{PTR}{100}=\frac{100\times 2\times 15}{100}=130%

44%——–>2860

100%——–>?

\frac{2860\times 100}{44}=6500

\frac{6500\times 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 \frac{9}{10}    :        3\times \frac{6}{5}

1              :            2

\frac{1}{1}\times 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 20}{100}=44%

44+20+\frac{44\times 20}{100}=72.8%

72.8-45=27.8%

27.8%——–>417

100%———->?

\frac{417\times 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 \frac{x}{100}=6.8

x= \frac{6.8\times 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 \frac{1}{8}\times \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 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 10}{100}=21%

R=21% T=2 years

21+21+\frac{21\times 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 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 20}{100} = 44%

second offer 20% compounded half yearly

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

10+10+\frac{10\times 10}{100}=21%

21+21+\frac{21\times 21}{100}=46.41%

46.41 – 44=2.41%

100%———->3600

2.41%———>?

\frac{3600\times 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 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 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 216}{7}=12960 is principle