A If 6000 is invested at an annual rate of 105 compounded co

A: If $6000 is invested at an annual rate of 10.5% compounded continuously, what is the account balance after 3 years? (Round to the nearest penny)

B: If $6000 is invested at an annual rate of 10.5% compounded semiannually, what is the account balance after 3 years? (Round to the nearest penny)

Solution

Account balance will be : A = Pe^rt

(This is the formula for continuous compund interest)

Where P = 6000 $

r= 10.5 /100

t= 3 years

A = 6000 e ^((10.5 * 3)/100) = 8221.56= 8221 $ 56 penny (ans)

B) For semi annual compound interest: after 3 years account balance A will be:

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

where n = 2 (semi annually means interstwill be compounded 12/6 = 2 times)

= 6000 (1+(10.5/100)/2))^2 . 3

= 8156 .13

= 8156 $ 13 penny (ans)