Future value of an annuity for various compounding periods

find the future values of the following ordinary annuities.

fv of $600 each 6 months for 7 years at a nominal rate of 12%, compounded semiannually. do not round intermediate calculations. round your answer to the nearest cent.

$

fv of $300 each 3 months for 7 years at a nominal rate of 12%, compounded quarterly. do not round intermediate calculations. round your answer to the nearest cent.

$

the annuities described in parts a and b have the same amount of money paid into them during the 7-year period, and both earn interest at the same nominal rate, yet the annuity in part b earns more than the one in part an over the 7 years. why does this occur?
please help me on that

You want to know the future value of an annuity if $1200 per year is contributed for 7 years and interest is 12%. The first annuity has payments made and interest compounded 2 times per year. The second annuity has payments made and interest compounded 4 times per year.

You also want to know why the second annuity earns more than the first.

Future value

The future value of these annuities can be found using the annuity formula, or using a financial calculator. The formula is ...

FV = P(n/r)((1 +r/n)^(nt) -1)

(a)

For a payment of 600 twice a year for 7 years at an interest rate of 12%, this is ...

FV = 600(2/0.12)((1 +0.12/2)^(2·7) -1) = 600(21.01506593) ≈ 12,609.04

(b)

For a payment of 300 four times per year, the same calculation gives ...

FV = 300(4/0.12)((1 +0.12/4)^(4·7) -1) = 300(42.93092252) ≈ 12,879.28

(c)

The future value of annuity A is equivalent to about 10.508 payments of $1200. That is, the interest effectively added 3.508 annual payments to the value paid in.

The future value of annuity B is equivalent to about 10.733 payments of $1200. The interest effectively added 3.733 annual payments to the value paid in.

The additional value comes from compounding interest more frequently.

For annuity B, the interest paid after 6 months is computed on both the account value and the interest that was paid after 3 months. The interest computation for annuity A is based only on the account value, so is a little less. That difference adds up over time.