Jarvis wants to invest equal semiannual payments in order to have $10,000 at the end of 20 years. Assuming that Jarvis will earn interest at an annual rate of 6% compounded semi-annually, how would the periodic payment be calculated?

$10,000 divided by the future amount of an ordinary  annuity of 40 payments of $1 each at an interest rate of  3% per period.

Explanation:

given data

semiannual payments = $10,000

time period = 20 year

annual rate = 6%

solution

The question has future value because it calculates the periodic amount of the annual amount that must be invested to produce the given amount in the future.

Accordingly, the appropriate factor showing the effect of compound interest is derived from the formula for the future value of the common annuity of $1

This factor multiplied by the periodic payment is equal to the future amount. If the payment is unknown, the future amount of the regular annuity formula can be calculated by dividing the future amount ($ 10,000) by the appropriate factor obtained.

when payment is made semiannually for 20 years,

then 40 compounding period is involved.

If the interest rate is 6% the semiannual interest rate is 3%.