COMPOUND INTEREST

COMPOUND INTEREST

·          Interest is payable periodically on the principal and accumulated part of interest.

More interest can be earned by increasing the number of compounding per year.

The time period between which the interest is added to the account is called the compounding period.

Formula

Accumulated Amount (A) = P (1+r/n)^nt

Where :

P = Principal

r = Interest rate per annum in percentage expressed as fraction (6% =  0.06)

n = Number of times per year that interest is compounded

t = Number of years invested

A = Accumulated amount (Principal + Interest)

Question 1

Raju invested Rs 10,000 in a fixed deposit for 1 year at a compound interest rate of 6% per annum. Find out the accumulated amount after one year if

A.    Interest is compounded annually

B.    Interest is compounded semi annually

C.    Interest is compounded quarterly

D.   Interest is compounded monthly

E.    Interest is compounded weekly

Which method of compounding is advantageous?

Option A

DATA
Principal	10,000
Rate	0.06
Time	1 year
Compounding	Annually

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

   = 10,000 * (1+0.06/1)^1*1

   = 10,000 * (1.06)

   = Rs. 10,600

Option B

DATA
Principal	10,000
Rate	0.06
Time	1 year
Compounding	Semi Annually

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

   = 10,000 * (1+0.06/2)^2*1

   = 10,000 * (1+0.03)²

   = 10,000 * (1.03)²

   = 10,000 * 1.03 * 1.03

   = 10,000 * 1.0609

   = Rs. 10,609

Option C

DATA
Principal	10,000
Rate	0.06
Time	1 year
Compounding	Quaterly

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

   = 10,000 * (1+0.06/4)^4*1

   = 10,000 * (1+0.015)⁴

   = 10,000 * (1.015)⁴

   = 10,000 * 1.015 * 1.015 * 1.015 * 1.015

   = 10,000 * 1.0613

   = Rs. 10,613

Option D

DATA
Principal	10,000
Rate	0.06
Time	1 year
Compounding	Monthly

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

   = 10,000 * (1+0.06/12)^12*1

   = 10,000 * (1+0.005)¹²

   = 10,000 * (1.005)¹²

   = 10,000 * 1.0616

   = Rs. 10,616

Option E

DATA
Principal	10,000
Rate	0.06
Time	1 year
Compounding	Weekly

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

   = 10,000 * (1+0.06/52)^52*1

   = 10,000 * (1+0.0011)⁵²

   = 10,000 * (1.00115384615)⁵²

   = 10,000 * 1.0618

   = Rs. 10,618

SUMMARY

OPTION	COMPOUNDING PERIOD	ACCUMULATED AMOUNT
		Rs.
A	Annually	10,600
B	Semi Annually	10,609
C	Quarterly	10,613
D	Monthly	10,616
E	Weekly	10,618

Option E is advantageous because more interest is earned by increasing the compounding periods per year.