We can solve this problem using the formula for the future value of an annuity:
\[A = P \times \left( \dfrac{(1 + r)^n - 1}{r} \right)\]
Where:
A = Total value of the annuity
P = Amount invested at the end of each payment period
r = Interest rate per period
n = Number of payment periods
In this case,
P = $258
r = 6% per year = 6/100 = 0.06 per quarter
n = 21 years * 4 quarters = 84 quarters
Let's substitute these values into the formula and calculate the total value of the annuity:
\[ A = 258 \times \left( \dfrac{(1 + 0.06)^{84} - 1}{0.06} \right) \]
Using a calculator, we find that
\[ A \approx \$27,855.76 \]
Therefore, the total value of the annuity in 21 years will be approximately $27,855.76.
To save money for his daughter's college tuition, Shen invests $258 every quarter in an annuity that pays 6% interest, compounded quarterly. Payments will be made at the end of each quarter. Find the total value of the annuity in 21 years.
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