Final answer:
To calculate the monthly deposit needed to reach a future value of $109,010 in 17 years with a 3% APR with monthly compounding, you use the future value of an annuity formula, convert the APR to a monthly rate, and use financial calculations to solve for the monthly deposit required.
Step-by-step explanation:
To determine how much should be deposited monthly into a fund with a 3% APR with monthly compounding to achieve a future value of $109,010 after 17 years, you can use the future value of an annuity formula:
FV = P × [((1 + r)n - 1) / r]
Where:
FV is the future value = $109,010
P is the monthly payment (what we're solving for)
r is the monthly interest rate (APR divided by 12)
n is the total number of payments (years × 12)
First, we convert the APR to a monthly rate by dividing by 12:
Monthly rate = [3% / (100 × 12)] = 0.0025
Then, we calculate n:
n = 17 years × 12 months/year = 204
Now we can use the future value of an annuity formula to solve for P:
109,010 = P × [((1 + 0.0025)204 - 1) / 0.0025]
This requires using a financial calculator or solving for P algebraically.
Once P is calculated, that will be the monthly deposit required to reach $109,010 in 17 years with the given interest rate and compounding.