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 Compound Interest Questions

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FACTS  AND  FORMULAE  FOR  COMPOUND  INTEREST  QUESTIONS

 

 

Let Principal = P, Rate = R% per annum, Time = n years.

I.

1.  When interest is compound Annually:

Amount =P1+R100n

2.  When interest is compounded Half-yearly:

Amount = P1+(R2)1002n

3.  When interest is compounded Quarterly:

Amount = P1+R41004n

 

II.

1.  When interest is compounded Annually but time is in fraction, say 325 years.

Amount = P1+R1003×1+25R100

2.  When Rates are different for different years, say R1%, R2%, R3% for 1st, 2nd and 3rd year respectively.

Then, Amount = P1+R11001+R21001+R3100

 

III.  Present worth of Rs. x due n years hence is given by:

Present Worth = x1+R100n

Q:

What will Rs.1500 amount to in three years if it is invested in 20% p.a. compound interest, interest being compounded annually?

A) Rs.2592 B) Rs.2492
C) Rs.2352 D) Rs.2352
 
Answer & Explanation Answer: A) Rs.2592

Explanation:

The usual way to find the compound interest is given by the formula A = .p(1+r/100)^n

In this formula,

A is the amount at the end of the period of investment

P is the principal that is invested

r is the rate of interest in % p.a

And n is the number of years for which the principal has been invested.

In this case, it would turn out to be A =1500(1+20/100)^3

= 2592.

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Q:

The present worth of Rs.169 due in 2 years at 4% per annum compound interest is

A) Rs.156.25 B) Rs.150
C) Rs.140 D) Rs125.25
 
Answer & Explanation Answer: A) Rs.156.25

Explanation:

 

Present Worth

 

=P1+R1002

 

=1691+41002

 

= Rs.156.25

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29 23679
Q:

A man invests Rs.5000 for 3 years at 5% p.a. compound interest reckoned yearly. Income tax at the rate of 20% on the interest earned is deducted at the end of each year. Find the amount at the end of the third year

A) Rs.5624.32 B) Rs.5423
C) Rs.5634 D) Rs.5976
 
Answer & Explanation Answer: A) Rs.5624.32

Explanation:

 

 

 

5% is the rate of interest. 20% of the interest amount is paid as tax.

 

i.e  80% of the interest amount stays back.

 

 if we compute the rate of interest as 80% of 5% = 4% p.a., we will get the same value.

  

The interest accrued for 3 years in compound interest = 3 x simple interest on principal + 3 x interest on simple interest + 1 x interest on interest on interest.

 

= 3 x (200) + 3 x (8) + 1 x 0.32 =600 + 24 + 0.32 = 624.32

 

 

 

The amount at the end of 3 years = 5000 + 624.32 = 5624.32

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Q:

The compound interest on a sum of money for 2 years is rs.832 and the simple interest on the same sum for the same period is rs.800 .the difference between the compound interest and simple interest for 3 years

A) Rs.48 B) Rs.66.56
C) Rs.98.56 D) None of these
 
Answer & Explanation Answer: C) Rs.98.56

Explanation:

difference in C.I and S.I in 2years =Rs.32

S.I for 1year =Rs.400

S.I for Rs.400 for one year =Rs.32

rate=[100*32)/(400*1)%=8%

difference between in C.I and S.I for 3rd year

=S.I on Rs.832= Rs.(832*8*1)/100=Rs.66.56

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Q:

If you deposit $4000 into an account paying 6% annual interest compounded quarterly, how much money will be in the account after 5 years ?

A) 3387.42 B) 4387.42
C) 5387.42 D) 6387.42
 
Answer & Explanation Answer: C) 5387.42

Explanation:

The mathematical formula for calculating compound interest depends on several factors. These factors include the amount of money deposited called the principal, the annual interest rate (in decimal form), the number of times the money is compounded per year, and the number of years the money is left in the bank.

 FV=p1+rnnt

 

FV = Future value of the Deposit

 

p = Principal or Amount of Money deposited

 

r = Annual Interest Rate (in decimal form )

 

n = No of times compounded per year

 

t = time in years

FV=40001+0.0644(5)= 5387.42

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Q:

Rs. 5887 is divided between Shyam and Ram, such that Shyam's share at the end of 9 years is equal to Ram's share at the end of 11 years, compounded annually at the rate of 5%. Find the share of Shyam.

A) 3567 B) 3452
C) 3087 D) 3544
 
Answer & Explanation Answer: C) 3087

Explanation:

Shyam's share * (1+0.05)9 = Ram's share * (1 + 0.05)11

Shyam's share / Ram's share = (1 + 0.05)11 / (1+ 0.05)9 = (1+ 0.05)2 = 441/400

Therefore Shyam's share = (441/841) * 5887 = 3087

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Q:

If the compound interest on a certain sum at 1623% to 3 years is Rs.1270, find the simple interest on the same sum at the same rate and f or the same period.

A) 1080 B) 1090
C) 1180 D) 1109
 
Answer & Explanation Answer: A) 1080

Explanation:

Let the sum be Rs. x. Then,

 

 C.I=x*50300*1003-x=343x216-x=127x216 

 

⇔127x216=1270 

 

x=2160 

 

Thus, the sum is Rs. 2160

 

 S.I=Rs.2160*503*3*1100=Rs 1080

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Q:

In what time will Rs. 1000 become Rs. 1331 at 10% per annum compounded annually?

A) 1years B) 2years
C) 3years D) 4years
 
Answer & Explanation Answer: C) 3years

Explanation:

Principal = Rs. 1000; Amount = Rs. 1331; Rate = 10% p.a. Let the time be n years. Then,
[ 1000 (1+ (10/100))^n ] = 1331 or (11/10)^n = (1331/1000) = (11/10)^3
n = 3 years

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