da answer:
a. To determine the periodic deposit, we can use the formula for the future value of an ordinary annuity:
Future Value = Payment × [(1 + r)^n - 1] / r
Where:
- Future Value is the financial goal of $25,000.
- Payment is the periodic deposit we want to find.
- r is the interest rate per compounding period, which is 3.5% divided by 4 (quarterly compounding).
- n is the total number of compounding periods, which is 5 years multiplied by 12 (monthly compounding).
Using the formula, we can plug in the values:
$25,000 = Payment × [(1 + 0.035/4)^(5*12) - 1] / (0.035/4)
Solving for Payment, we find:
Payment = $25,000 × (0.035/4) / [(1 + 0.035/4)^(5*12) - 1]
b. To determine how much of the financial goal comes from deposits and how much comes from interest, we can subtract the total amount of deposits made from the final financial goal.
The total amount of deposits made can be calculated by multiplying the periodic deposit by the total number of deposits made over the 5-year period. The total number of deposits can be calculated by dividing the total number of months (5 years multiplied by 12) by the frequency of deposits (3 months).
Let's assume the periodic deposit is calculated to be $X using the formula in part a.
The total number of deposits made would be (5 years * 12 months) / 3 months = 20 deposits.
The total amount of deposits made would be $X * 20 deposits = $Y.
To determine the amount that comes from interest, we subtract $Y from the financial goal of $25,000:
Amount from interest = $25,000 - $Y.
Therefore, the amount from deposits is $Y and the amount from interest is $25,000 - $Y.
Remember, this calculation assumes that the periodic deposit remains the same over the entire 5-year period and the interest rate remains constant.
hope this helps ig <3