Question

Answer question 4 and 5.

An INDIVIDUAL is entitled to receive an annual end-of- end of the 20-year period, annual payments will pass to to accumulate funds to provide a retirement annuity for its Vice Preside Upon retirement, she is entiearch, Jil G Sunrise industries wishes year payment of $44,000 for exactly 20 years. If she dies prior to the her heirs Ms. Garza, by contract, will retire at the end of exactly 12 years into an account earning 9% interest. Once the 20-year-disbursement period" begins, Sunrise plans to monies During the 12-year "accumulation period" Sunrise wishes to fund the annuity by making equal, annual, end-of into an into an account earning a guaranteed 8% per year. At the end of te that the first deposit will be made at the end of Year 1 and that the the distribution period, the account balance will be first distribution payment wil be received at the end of Year 13.

Answer 1

As only Q4 and Q5 are required, the solution will be regarding the same.

In the given question, the timeline is as follows:

Accumulation Period (12 years) Disbursement Period (20 years) Time 0 T12 T 32 Amount to be paid: $44,000 p.a.

Q4)

The question asks us to calculate the equal, annual end of year deposits, given the total amount needed at the end of 12 years is $450,000. We need to find these annual deposits, given a return of 10%.

Thus, we shall use the FVA formulas as described below:

FVA = A* ({[(1+r)^n] -1}/r)

$450,000 = A* ({[(1.10)^12] -1}/0.10)

Annuity amount = $ 21,043.48

Q5)

The question requires us to calculate Q2 and Q3 assuming payments made to Ms. Graza would be at the beginning to the year. This would result in a slight change of formula.

(a) Size of the accumulated amount

To calculated the accumulated amount, we use the following PVA formula:

PVA = A* {(1/r) - [1/(r*(1+r)^n)]} * (1+r)

The (1+r) is used to adjust for the beginning of the year payments to be made.

PVA = $44,000* {(1/0.08) - [1/(0.08*(1.08)^20)]} * (1.08)

PVA = $ 466,558.37

Thus, Sunrise Industries needs to accumulate $466,558.37 at the end of the accumulation phase, to fund $44,000 beginning of the year payments for the next 20 years.

Note: The question states that only payments made to Ms. Graza are at the beginning of the year. Deposits by Sunrise Industries are the end of the year (as nothing is mentioned of its change).

(b) Size of the "accumulation period" end-of-year annuity

To solve this, we will use the FVA formula as stated below:

FVA = A* ({[(1+r)^n] -1}/r)

$ 466,558.37 = A* ({[(1.09)^12] -1}/0.09)

Annuity amount = $ 23,164.95