Final answer:
To find the amount needed to deposit at the beginning of the 2-year period, we can use the formula for the future value of an ordinary annuity. The amount to be deposited at the beginning is $14,825.01. The amount of what you receive that will be interest is $2,165.29.
Step-by-step explanation:
To find the amount needed to deposit at the beginning of the 2-year period, we can use the formula for the future value of an ordinary annuity:
PV = PMT * [(1 + r)^n - 1] / r
Where PV is the present value (amount to be deposited), PMT is the monthly payment ($650), r is the interest rate per period (7.5% divided by 12), and n is the number of periods (2 years multiplied by 12).
Substituting the values into the formula, we get:
PV = $650 * [(1 + 0.075/12)^(2*12) - 1] / (0.075/12)
Simplifying the equation, we find that the amount to be deposited at the beginning is $14,825.01.
To calculate the amount of what you receive that will be interest, we can subtract the principal (amount deposited) from the total amount received over the 2-year period. The total amount received can be found using the formula for the future value of an annuity:
FV = PV * (1 + r)^n
Substituting the values into the formula, we get:
FV = $14,825.01 * (1 + 0.075/12)^(2*12)
Calculating the future value, we find that the total amount received over the 2-year period is $16,990.30. Subtracting the amount deposited ($14,825.01) from the total amount received, we find that $2,165.29 will be interest.