Final answer:
Ingrid must deposit approximately $463.04 at the end of each quarter into an account paying 5.9% interest compounded quarterly to have $20,000 in 8 years.
Step-by-step explanation:
To determine how much Ingrid must deposit at the end of each quarter to save for a $20,000 car in 8 years with an account paying 5.9% interest compounded quarterly, we need to use the future value of an annuity formula, which is given as:
FV = P × { [(1 + r)^n - 1] / r }
Where FV is the future value of the annuity, P is the annuity payment per period, r is the interest rate per period, and n is the total number of periods.
First, convert the annual interest rate to a quarterly rate by dividing it by 4, since there are 4 quarters in a year:
r = (5.9% / 4) / 100 = 0.01475 per quarter
Next, calculate the total number of periods (quarters) in 8 years:
n = 8 years × 4 quarters/year = 32 quarters
Now, rearrange the annuity formula to solve for P:
P = FV / { [(1 + r)^n - 1] / r }
Plugging the values we have into the formula, we get:
P = $20,000 / { [(1 + 0.01475)^32 - 1] / 0.01475 }
Finally, calculate the amount to be deposited each quarter:
P = $20,000 / { [(1 + 0.01475)^32 - 1] / 0.01475 } = $463.04
Ingrid must deposit approximately $463.04 at the end of each quarter to have $20,000 in 8 years.