Answer:
(a) The deposit should be <u>$168.06 </u>quarterly.
(a) The deposit should be <u>$145.32 </u>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
