Compound Interest?

Question

Find the effective annual rate of interest on $1000 at 8% compounded;

a) quarterly
b) continuously

Answer 1

If r is the effective annual rate of interest, after t years a principal of $1000 will have value

$1000(1 + r)^t

a) For quarterly periods we divide r by 4 and multiply t by 4.

The value of $1000 after t years compounded quarterly at 8% is

$1000(1 + 0.08/4)^4t = 0.0824 or 8.24%


b) The value of $1000 after t years compounded continuously at 8% is

$1000e^0.08t

If r is the effective annual rate of interest

$1000(1 + r)^t = $1000e^0.08t = 0.0833 or 8.33%

Answer 2

CI is compound interest
P= Principal = 1000
R = R% per annum = 8% pa = 2% quaterly
T= 1yr, n= 4 quaters
A= P(1+R)^n
A= 1000 *51/50* 51/50*51/50*51/50
cALCULATE THIS nd sub 1000 from it.

Answer 3

Effective Annual Interest = (1+(interest rate/(no.of compounding periods))^no.of compounding periods)-1

Therefore,

Quarterly = (1+0.08/4)^4 - 1 which gives 8.24%

Continuously = (1+0.08/365)^365 - 1 which gives 8.33%