LAST TIME REVISION (INTREST)-1
INTEREST
A payment, from a borrower to a lender of an amount above repayment of the principal sum (that is the amount borrowed) at particular rate, is called interest.
There are two types of interest.
SIMPLE INTEREST
When interest is calculated only borrowed money for definite period, then such interest is called simple interest and is denoted by SI .
SI= (Px R xT)/100
and A = P(1+ RT/100)= P+ SI
Where, P= principal
R= Rate of Interest
T= time
A= Amount
COMPOUND INTEREST
Compound interest (or compounding interest) is the interest calculated on the initial principle, which also includes all of the accumulated interest from previous periods on a deposit or sum. It is denoted by CI.
A= P(1+ R/100)ⁿ and
CI= P[(1+ R/100)ⁿ -1]
Where A= amount
P= principal
R= Rate
n= times
There are following two special case.
i) When interest is calculated per half yearly in a compound interest , then rate of interest must be divided by 2 and time must be multiplied by 2. Then, R= R/2 and n= 2n.
ii) When interest is calculated per quarterly in compound interest , then rate of interest must be divided by 4 and time must be multiplied by 4 for calculation of intrest.
then= R= R.4 and n=4n.
IMPORTANT FORMULAE
1) If a sum of money becomes n times in T year at a simple interest, then rate of interest will be given as
R= {100(n -1)%/T}
2) If a sum of money at a certain rate of interest becomes N₁ times in T₁ yr and N₂ times in T₂ yr, then
T₁/T₂ = (N₁ -1)/(N₂ -1)
3) When rate of interest for 3 consecutive years are r₁% , r₂% , and r₃% respectively. Then,
Amount (A)= P(1+ r₁/100)(1+ r₂/100)(1+ r₃/100)
4) If intrest is compounded annually but time is in mixed fraction (like n-a/b yr), then
Amount (A)= P(1+ r/100)ⁿ [1+ (a/b) xr /100]
5) If a certain sum at compound interest becomes x times in n₁ yr and y times in n₂ yr, then
ₓ(1/n₁) = ᵧ(1/n₂).
6) The difference between compound interest and simple interest obtained on Rs P at r% per annum for 2 yr, then
Difference (D)= P(r/100)²
7) The difference between compound interest and simple interest obtained on Rs P at r% per annum for 3 years, then
Difference (D)= Pr²(300+r)/(100)³
INSTALLMENT
When a borrower paid the total money in some equal parts, i.e, not in the single amount, then we say that he/she is paying in installment.
For simple interest
A= [x + (x + (x .R. 1)/100) +(x + (x. R. 2)/100) +....]
Where
A= Total amount to be paid
x= Value of each installment
R= Rate of interest
For compound interest
A= [x/(1 + R/100) + x/(1+ R/100)² +....]
where,
A= total amount to be paid
x= value of each installment
R= rate of interest
a) 4000 b) 5000 c) 2500 d) 4500
2) A sum becomes Rs8800 in 4 years at simple interest at the yearly interest rate of 25% per annum. What is the sum?
a) 4400 b) 6600 c) 7040 d) 6400
3) Simple interest on a sum of Rs1400 for 3 years and 4 months is Rs700. What is the rate (in percentage) of interest per annum ?
a) 17 b) 15 c) 18 d) 12
4) The compound interest on a certain sum of money for 2 years at 5% is Rs328, then the sum is
a) 3000 b) 3600 c) 3200 d) 3400
5) At what rate of compound interest per annum will a sum of Rs2000 becomes Rs23328 in 2 years ?
a) 8% b) 16% c) 24% d) 12%
6) Rs10000 is kept at compound interest at the rate of 18% per annum compounding annually. If the compounding of interest is done half yearly, then how much more interest will be obtained ?
a) 243 b) 324 c) 81 d) 162
7) What annual installment will discharge dept of Rs1696 in 4 years at 4% per annum simple interest ?
a) 525 b) 425 c) 325 d) 400
8) In how many years shall Rs3500 invested the rate of 10% simple interest per annum, amount to Rs4500 ?
a) 19/5yr b) 17/7yr c) 18/7yr d) 20/7yr
9) A borrows a sum Rs1000 from his friends B on 31st December 2015 on the condition that he will return the same after 1 year with simple interest at 12%. However , A gets into a position of returning the money on 1 May 2016. How much amount he has to return to B?
a) 1331.5 b) 1045 c) 1120 d) 1040
10) A certain amount invested at a certain rate, compound annually, grows to an amount in 5 years, which is a factor of 1.1881 more than to what it would have grown in 3 years. What is the rate percentage?
a) 9 b) 8.1 c) 8 d) 9.2
11) The difference between compound interest and simple interest on Rs x at 6.5% per annum for 2 years is
a) 7800 b) 7500 c) 8000 d) 8500
12) The compound interest on a certain sum of money at 21% for 2 years is 9282, its simple interest at same rate and for the same period is
a) 8750 b) 8400 c) 8000 d) 8500
13) simple interest on a sum for 8 months at 6% per annum is Rs340. What is the value of sum ?
a) 8500 b) 9500 c) 8000 d) 6800
14) A sum becomes Rs1392 in 2 years and Rs1488 in 3 years at simple interest. What is the rate (in percentage) of interest per annum ?
a) 8 b) 10 c) 12 d) 8.5
15) A person borrows some money for 4 years at the rate of simple interest. If the ratio of principle and total interest is 5:1, then what is the rate of interest?
a) 5 b) 25 c) 10 d) 20
16) A sum of Rs7500 is divided into two parts. The simple interest on first part at the rate of 12% per annum is equal to the simple interest on second part at the rate of 18%. What is the interest on each part of 1 year ?
a) 600 b) 360 c) 480 d) 540
17) An equal sum is invested in two different schemes. One scheme gives simple interest and the other gives compound interest (annual compounding). The total interest obtained after 2 years from both the schemes together is Rs2090. If both the schemes have 18% per annum interest rate, then what is the first year interest scheme?
a) 1000 b) 500 c) 545 d) 1045
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