you deposit $3,500 in a savings account that pays 7.5% interest compounded semiannuallyHow much interest does the account earn in the first six months?

Question

i dont understand this question and i need help

Answer 1

Actually, the interest, while compounded semi-annually,

totals to 7.5% for the year.  The total earned in 6 months

will be half that amount or $131.25

 

A = P(1+r/n)^nt  is the formula for compound interest

A = future amount

P = principal investment - $3500

r = interest rate as a decimal = .075

n = # times compounded each year = 2

t = time in years = 1/2  or  .5 since we are looking for 6 months

 

A = 3500(1+.075/2)^2(.5) = 3500(1.0375)= $3631.25

 

The interest earned in this 6 month period will be the

difference between the final amount and the principal..

I = A-P = 3631.25 - 3500  = $131.25

Answer 2

This means that the account gains 7.5% in interest every six months (semi-annually).  So after the first six months, it's simply gone up 7.5%.  So it has earned:

 

3500 * .075 = $262.50 after the first six months.

 

Sounds like a great investment to me! : )

 

Hope this helps, Gorgia!