Question

If $500 is invested at an interest rate of 5.5% per year, find the amount of the investment at the end of 15 years for the following compounding methods. (Round your answers to the nearest cent.) A.) Annually: $ B.) Semiannually: $ C.) Quarterly: $ D.) Continuously: $

Answer 1

Formula for compound interest is:

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

Where,

A= final amount

P= principal (here 500)

R= rate of interest (here 0.055)

n= no. of times the compounding is done in an year

t= time in years (here 15)

A. Since money is compounded annually in this part:

n=1

A= 500* (1+0.055/1)^(1*15)

= $1116.24

B. Since money is compounded semiannually

n=2

A= 500*(1+ 0.055/2)^(15*2)

= $1128.301

C. Since money is compounded quarterly

n=4

A= 500*(1+0.055/4)^4*15)

=$1134.55

D. As compounding is done continuously

Amount= Principal* (e^r*t)

Where,

r= rate(here 0.055)

t= time(here 15)

Amount = 500e^(0.055*15)

= $1140.94