Final answer:
To find out how long it takes to save $10,500 with semiannual deposits of $850 in a savings account that earns 3.72% compounded quarterly, the future value of an annuity formula must be used with adjustments to match different compounding and payment frequencies. The exact time cannot be provided without solving an equation using the given values.
Step-by-step explanation:
To determine how long it would take to save at least $10,500 by making deposits of $850.00 at the end of every 6 months in a savings account that earns 3.72% compounded quarterly, one would have to use the future value of an annuity formula:
FV = P * [(1 + r/n)^(nt) - 1] / (r/n)
Where:
- FV is the future value of the annuity.
- P is the periodic payment amount.
- r is the annual interest rate in decimal form.
- n is the number of times the interest is compounded per year.
- t is the number of years.
However, because the payments are semiannual and the interest is compounded quarterly, the formula needs adjustment. Payments are made every six months (2 times per year), and the interest is compounded four times per year. The future value of an annuity formula must be altered to match the compounding period with payment frequencies.
Unfortunately, we cannot simply provide the exact number of years and days without setting up and solving an equation using the given values and the appropriate variation of the formula, potentially through iterative methods or financial calculator functions since the deposit frequency and the compound interest frequency do not match.