Final answer:
To find the monthly deposit that Logan must make to have $100,000 in 20 years at a 7.1% interest rate compounded monthly, use the future value of an annuity formula. Once the formula is applied with the given values, it yields the monthly savings amount matching one of the provided options.
Step-by-step explanation:
The question asks how much Logan must deposit every month into an account with an annual interest rate of 7.1%, compounded monthly, to have $100,000 saved in 20 years. To solve this, we need to use the formula for the future value of an annuity compounded monthly:
FV = P × {[(1 + r/n)^(nt) - 1] / (r/n)}
Where:
- FV is the future value of the investment
- P is the monthly deposit
- r is the annual interest rate (decimal)
- n is the number of times the interest is compounded per year
- t is the number of years
For Logan, FV is $100,000, r is 0.071 (7.1%), n is 12 (since it's compounded monthly), and t is 20 years. By rearranging the formula to solve for P, we get:
P = FV / {[(1 + r/n)^(nt) - 1] / (r/n)}
After substituting the given values into the formula and calculating, we determine the monthly savings required. Consequently, the correct answer is one of the given options, matching the result of our calculation.