(a) What amount should be deposited in a fund at the end of each quarter at 7% compounded quarterly so that there will be enough money in the fund? (b) Find the investors quarterly deposit if the money is deposited at 94% compounded quarterly.
The deposit should be. $ (Round to the nearest cent as needed)

(a) The deposit should be $168.06 quarterly.

(a) The deposit should be $145.32 quarterly.

Explanation:

Note: This question is not complete. The complete question is therefore provided before answering the question as follows:

An investor needs $11,000 in 19 years.

(a) What amount should be deposited in a fund at the end of each quarter at 7% compounded quarterly so that there will be enough money in the fund?

(b) Find the investors quarterly deposit if the money is deposited at 9.4% compounded quarterly.

The explanations to the answers are now given as follows:

(a) What amount should be deposited in a fund at the end of each quarter at 7% compounded quarterly so that there will be enough money in the fund?

Since the amount should be deposited in a fund at the end of each quarter, the formula for calculating the Future Value (FV) of an Ordinary Annuity is used as follows:

FV = M * {[(1 + r)^n - 1] / r} (1)

Where,

FV = Future value of the amount needed in 19 years = $11,000

M = Quarterly deposit = ?

r = Quarterly interest rate = 7% / 4 = 0.07 / 4 = 0.0175

n = number of quarters the deposits will be made = 11 * 4 = 44

Substituting the values into equation (1) and solve for M, we have:

11,000 = M * {[(1 + 0.0175)^44 - 1] / 0.0175}

11,000 = M * 65.4531536741798

M = 11,000 / 65.4531536741798

M = $168.06

(b) Find the investors quarterly deposit if the money is deposited at 9.4% compounded quarterly.

We make use of equation (1) in part (a) as follows:

Where,

FV = Future value of the amount needed in 19 years = $11,000

M = Quarterly deposit = ?

r = Quarterly interest rate = 9.4% / 4 = 0.094 / 4 = 0.0235

n = number of quarters the deposits will be made = 11 * 4 = 44

Substituting the values into equation (1) and solve for M, we have:

11,000 = M * {[(1 + 0.0235)^44 - 1] / 0.0235}

11,000 = M * 75.6957891651599

M = 11,000 / 75.6957891651599

M = $145.32

answer; false pretense;