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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:

How much money would you need to deposit today at 9% annual interest compounded monthly to have $12000 in the account after 6 years?

A) 9007 B) 4007
C) 7007.08 D) 8oo7
 
Answer & Explanation Answer: C) 7007.08

Explanation:

FV=P(1+r/n)^nt

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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 4526
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 4508
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 4500
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 4487
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 4476
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 4418
Q:

Kramer borrowed $4000 from George at an interest rate of 7% compounded semiannually. The loan is to be repaid by three payments. The first payment, $1000, is due two years after the date of the loan. The second and third payments are due three and five years, respectively, after the initial loan. Calculate the amounts of the second and third payments if the second payment is to be twice the size of the third payment.

A) 1389 B) 1359
C) 1379 D) 1339.33
 
Answer & Explanation Answer: D) 1339.33

Explanation:

Given:j=7% compounded semiannually making m=2 and i = j/m= 7%/2 = 3.5%
Let x represent the third payment. Then the second payment must be 2x.
PV1,PV2, andPV3 represent the present values of the first, second, and third payments.

Since the sum of the present values of all payments equals the original loan, then
PV1 + PV2  +PV3  =$4000 -------(1)

PV1   =FV/(1 + i)^n  =$1000/(1.035)^4=  $871.44

At first, we may be stumped as to how to proceed for
PV2 and PV3. Let’s think about the third payment of x dollars. We can compute the present value of just $1 from the x dollars

pv=1/(1.035)^10=0.7089188

PV2   =2x * 0.7089188 = 1.6270013x
PV3   =x * 0.7089188=0.7089188x
Now substitute these values into equation ➀ and solve for x.
$871.442 + 1.6270013x + 0.7089188x  =$4000

2.3359201x  =$3128.558

x=$1339.326
Kramer’s second payment will be 2($1339.326)  =$2678.65, and the third payment will be $1339.33

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