Sarah deposits $250 into an annuity due at the beginning of every 6-month period for 9 years. The account earns an annual 6% compounded semiannually. What is the future value of the annuity after 9 years? How much interest did she earn?

Answer: she earned $6007.5

Step-by-step explanation:

We would apply the formula for determining future value involving deposits at constant intervals. It is expressed as

S = R[{ (1 + r) ^n - 1) }/r][1 + r]

Where

S represents the future value of the investment.

R represents the regular payments made (could be weekly, monthly)

r = represents interest rate/number of interval payments.

n represents the total number of payments made.

From the information given,

R = $250

r = 0.06/2 = 0.03

n = 2 * 9 = 18

Therefore,

S = 250[{ (1 + 0.03) ^18 - 1) }/0.03][1 + 0.03]

S = 250[{ (1.03) ^18 - 1) }/0.03][1.03]

S = 250[{ (1.7 - 1) }/0.03][1.03]

S = 250[{ (0.7) }/0.03][1.03]

S = 250[23.3][1.03]

S = 250 * 24.03

S = $6007.5