Compound
Interest
* Amount = Principal + Interest
* Simple Interest = (Principal x Rate x Time)/100
* A = P Here A = amount, P = principal, r = rate percent
yearly (or every fixed period) and n is the number of years
(or terms of the fixed period).
* C.I. = P , where C.I. = compound interest
* If the interest rates for the successive fixed periods
are r1%, r2%, r3% ..., then A (amount) is given by
A=P...
* S.I. (simple interest) and C.I. (compound interest) are
equal for the first year (or the first term of the fixed period)
on the same sum and at the same rate.
* C.I. of 2nd year (or the second term of the fixed
period) is more than the C.I. of 1st year or the first term of
the fixed period), and C.I. of 2nd Year -C.I. of 1st year =
S.I. on the interest of the first year.
* Equal installments (with compound interest):
Loan amount = P
where P = each equal installment
R = rate of interest per annum (or per specified period)
T = time, say 3 years (or 3 specified terms).
Note. If T = n years (or specified terms), then there will
be n brackets.
Exercise1.1
1.A person invests Rs 5600 at 14%p.a compounded semi annually for 2
yrs.Calculate
a.the interest for the first year.
b.the amount at the end of the first year.
c.the interest for the 2nd year.
2.Calculate the amount and the compound interest on Rs 5000 for 2yrs hen
the rate of interest for successive years is 10%,9% respectively.
3.A person invests Rs 180000 for 3 yrs at a certain rate for
interest,compounded annually.at the end of one year it amounts to Rs
190000. Calculate
a.the rate of interest per annum.
b.the interest accrued in the second year.
c.the amount t the end of the third year.
4.On a certain sum of money ,invested at the rate of 10% p.a.compounded
annually,the interest for the first year plus the interest for the third year is
Rs 2,652.find the sum.
5.During every financial year,the value of a machine depriciates by
12%.find the original cost of a machine which depriciates by Rs2,640
during the second financial year of its purchase.
6.The C.I,calculated half-yearly,on a certain sum of money for the second
year is Rs 10,189 and for the third year it is Rs 11,297.Calculate the rate of
interest and the sum of money
7.If the interest is compounded half yearly,calculate the amount when
principal is Rs 7,400;the rate of interest is 5% p.a. and the duration is one
year.
8.On what sum of money will the C.I. for two and a half year at 10%
amount to Rs 676.25?
9.Mr.Kumar took a loan of Rs32,760 from a private finance company at
20% compounded annual instalments.Calculate the amount of each
instalment.
10.Findthe effective rate percent p.a. equivalent to a
normal rate of 13% p.a interest payable half-yearly?
11.Simple interest on a sum of money for 2yrs at 4% is Rs 500.find the
compound interest on the same sum and at the same rate for 1yrs,if the
interest is reckoned half-yearly.
12.Find the difference between compound interest on Rs 13000 for 1 and
a half a year at 16% p.a.when compounded annually and semi annually
and simple interest.
13.A saving certificate costs Rs 50,000 and is worth Rs 50,832 at the end
of two years.What rate % Compounded p.a. is allowed? How long would it
take Rs 25,500 to increase to Rs 31,149.28 at the same rate?
14.Divide Rs 8,400 into two parts such that the ratio between the amount
of the first part in 3years and the amount of the second part in 4years at
10% C.I.compounded yearly is 5:7.
15.A,B,and C are three persons with age 26,27,28 years.In what ratio must
they invest money at 14% compounded yearly so that each gets same
sum at the age of his retirement (i.e. at the age of 60 years).
16.A sum of money lent out at C.I. at a certain rate per annum doubles
itself in 5 years.Find in how many years will the money becomes eight
times of itself at the same rate of interest p.a.
Exercise1.2
17. In what time will a sum of Rs 800 at 10% per annum
compounded half-yearly produce Rs 126·10?
18. The simple interest on a sum of money for 2 years at 4% p.a.
is Rs 450. Find the compound interest on this sum of money at
the same rate
(i) for 1 year if the interest is reckoned semi-annually.
(ii) for 2 years if the interest is reckoned annually.
19. At what rate of compound interest will Rs 625 amount to Rs
729 after 2 years? Also find the maturity value of Rs 625 after 2
years at the above rate of simple interest.
20. Ram and Bhola each borrow equal sums for 3 years at 10%
p.a. simple interest and compound interest respectively. At the
time of repayment, Bhola has to pay Rs 372 more than Ram. Find
the sum borrowed and interest paid by each.
21. The difference between the compound interest for a year
payable half-yearly and the simple interest on a certain sum of
money lent out at 10% p.a. for a year is Rs 15. Find the sum of
money lent out.
22. The difference between compound interest and simple
interest in 3 years at 10% p.a. reckoned yearly is Rs 18·60. Find
the sum and the compound interest.
23. The amount at compound interest which is calculated yearly
on a certain sum of money is Rs 1250 in one year and Rs 1375 in
two years. Calculate the rate of interest.
24. A certain sum of money amounts to Rs 10584 in two years
and to Rs 11113·20 in three years, interest being compounded
annually. Find the interest rate percent and the original sum.
25. The compound interest and the simple interest on the same
sum of money at the same rate percent per annum are Rs 410
and Rs 400 respectively. Find the rate of interest and the sum of
money.
26. The compound interest calculated yearly on a certain sum of
money for the second year is Rs 880 and for the third year it is Rs
968. Find the rate of interest and the original money.
27. The simple interest on a certain sum for 3 years is Rs 150
and the compound interest on the same sum at the same rate for
2 years is Rs 110. Find the rate of interest and the principal.
28. A sum of money lent at C.I. on 1st April 96 amounts to Rs
2420 on 1st April 98 and to Rs 2662 on 1st April 99. Find the rate
of interest and the sum.
29. The simple interest in 3 years and the compound interest in 2
years on a certain sum at the same rate are Rs 1200 and Rs 832
respectively. Find
(i) the rate of interest, (ii) the principal,
(iii) the difference between C.I. and S.I. for three years.
30. The value of a machine depreciates every year at the rate of
10% of its value. The machine was purchased for Rs 40000 when
new and it was sold for Rs 29160. Find the number of years that
the machine was used.
31. A man borrowed a sum of money and agrees to pay off by
paying Rs 3150 at the end of the first year and Rs 4410 at the end
of the second year. If the rate of compound interest is 5% p.a.,
find the sum borrowed.
32. A man borrowed a certain sum of money and paid it back in 2
years in two equal instalments. If the rate of compound interest
was 4% p.a. and if he paid Rs 676 annually, what sum did he
borrow?
33. A sum of Rs 16400 is borrowed to be paid back in 2 years by
two equal annual instalments allowing 5% compound interest.
Find the annual payment.
34. A loan of Rs 4641 is to be paid back by 4 equal annual
instalments. The interest is compounded yearly at 10%. Find the
value of each instalment.
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