Part A: Total Account Balances
Year 0: $6,000 (initial principal)
Year 1:
Interest per quarter = (6,000 * 6% / 4) = $90
Interest for the year = $90 * 4 = $360
Account balance at year 1 = $6,000 + $360 = $6,360
Year 2:
Interest per quarter = ($6,360 * 6% / 4) = $95.40
Interest for the year = $95.40 * 4 = $381.60
Account balance at year 2 = $6,360 + $381.60 = $6,741.60
Year 3:
Interest per quarter = ($6,741.60 * 6% / 4) = $101.14
Interest for the year = $101.14 * 4 = $404.56
Account balance at year 3 = $6,741.60 + $404.56 = $7,146.16
Year 4:
Interest per quarter = ($7,146.16 * 6% / 4) = $107.19
Interest for the year = $107.19 * 4 = $428.76
Account balance at year 4 = $7,146.16 + $428.76 = $7,574.92
Part B: Function Type
Since the account balance grows exponentially due to compounding, the data is best modeled by an exponential function.
Part C: APY
APY (Annual Percentage Yield) takes into account the effect of compounding interest, unlike the nominal annual interest rate (6%). We can calculate the APY using the formula:
APY = [(1 + (nominal rate / n))^n - 1] * 100
where:
APY is the annual percentage yield
nominal rate is the annual interest rate (6%)
n is the number of compounding periods per year (4, for quarterly compounding)
Plugging in the values:
APY = [(1 + (6% / 4))^4 - 1] * 100
APY = [(1.015)^4 - 1] * 100
APY ≈ 0.0609 * 100
APY ≈ 6.09%
Therefore, the APY for this savings account is approximately 6.09%, slightly higher than the nominal annual interest rate due to compounding.
