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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 is the difference between the compound interests on Rs. 5000 for 112 years at 4% per annum compounded yearly and half-yearly?

A) Rs.3.06 B) Rs.2.04
C) Rs.3.65 D) Rs.5.40
 
Answer & Explanation Answer: B) Rs.2.04

Explanation:

 C.I. when interest compounded yearly

Rs.5000*1+4100*1+12*4100

 Rs.5000*2625*5150

=Rs.5034

 

C.I. when interest iscompounded half-yearly 

 Rs.5000*1+21003

= Rs. 5306.04

Difference = Rs. (5306.04 - 5304) = Rs. 2.04

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1 5030
Q:

Simon deposits $400 in an account that pays 3% interest compounded annually. What is the balance of Simon’s account at the end of 2 years?

A) 424.36 B) 524.56
C) 545.36 D) 456.36
 
Answer & Explanation Answer: A) 424.36

Explanation:

I=Prt

 

I=12

 

Balance = P +Prt

 

412

 

Find the balance at the end of the second year.

 

I = Prt=12.36

 

Balance =P + Prt

 

424.36

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0 4934
Q:

The population of a rural region is expected to fall by 2% per year for the next 10 years. If the region’s current population is 100,000, what is the expected population 10 years from now?

A) 81707 B) 91707
C) 61707 D) 71707
 
Answer & Explanation Answer: A) 81707

Explanation:

i=j/m

FV = PV(1 + i)^n

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2 4915
Q:

If the simple interest on a sum of money at 5% per annum for 3 years is Rs. 1200, find the compound interest on the same sum for the same period at the same rate.

A) Rs.1251 B) Rs.1261
C) Rs.1271 D) Rs,1281
 
Answer & Explanation Answer: B) Rs.1261

Explanation:

Clearly, Rate = 5% p.a .,

Time = 3 years

S.I =Rs.1200.

So,Principal

=Rs.(100 x 1200/3x5)

=Rs.8000.

 

Amount

=Rs.[8000 x (1+5/100)³]

=Rs(8000x21/20x21/20x21/20)

= Rs.9261

 

C.I

=Rs.(9261-8000)

=Rs.1261.

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1 4852
Q:

Payments of $2000 and $1000 were originally scheduled to be paid one year and five years, respectively, from today. They are to be replaced by a $1500 payment due four years from today, and another payment due two years from today. The replacement stream must be economically equivalent to the scheduled stream. What is the unknown payment, if money can earn 7% compounded semiannually?

A) 1548 B) 1348
C) 1648 D) 1748
 
Answer & Explanation Answer: C) 1648

Explanation:

FV1 = Future value of $2000, 1 year later
= PV (1+  i)^n

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2 4779
Q:

$10,000 face value strip bond has 15 years remaining until maturity. If the prevailing market rate of return is 6.5% compounded semiannually, what is the fair market value of the strip bond?

A) 1710.29 B) 2710.29
C) 3710.29 D) 4710.29
 
Answer & Explanation Answer: C) 3710.29

Explanation:

i=j/m

n =m(Term) = 2(15.5)  =31

Fair market value  Present value of the face value

 =FV(1+  i)^-n

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4 4751
Q:

If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same at the same rate and for the same time

A) Rs.51.25 B) Rs.61.25
C) Rs.51 D) Rs.42
 
Answer & Explanation Answer: A) Rs.51.25

Explanation:

Sum = Rs.(50*100)/2*5=Rs.500

Amount=Rs.[500*(1+5/100)2]

= Rs. 551.25

 

 C.I = Rs.(551.25-500)= Rs.51.25

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0 4711
Q:

Find the effective rate of interest for an investment that earns 5 1/2% per year, compounded continuously

A) 5.65% B) 5.75%
C) 5.85% D) 5.95%
 
Answer & Explanation Answer: A) 5.65%

Explanation:

We are not given a value of P in this problem, so either pick a value

for P and stick with that throughout the problem, or just let P = P.

We have that t = 1, and r = .055. To find the effective rate of interest,

first find out how much money we have after one year:

A = Pert

A = Pe(.055)(1)

A = 1.056541P.

Therefore, after 1 year, whatever the principal was, we now have 1.056541P.

Next, find out how much interest was earned, I, by subtracting the initial amount of money from the final amount:

I = A − P

  = 1.056541P − P

  = .056541P.

Finally, to find the effective rate of interest, use the simple interest formula, I = Prt. So,

I = Pr(1) = .056541P

.056541 = r.

Therefore, the effective rate of interest is 5.65%

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