Question

Calculate the annual cash flows of a $2 million, 10-year fixed-payment deferred annuity earning a guaranteed 8 percent per year if annual payments are to begin at the end of the sixth (6th) year.

Answer 1

To calculate the annual cash flows of a $2 million, 10-year fixed-payment deferred annuity earning a guaranteed 8 percent per year if annual payments are to begin at the end of the sixth (6th) year, we can use the present value formula.

Step-by-step explanation:

To calculate the annual cash flows of a $2 million, 10-year fixed-payment deferred annuity earning a guaranteed 8 percent per year if annual payments are to begin at the end of the sixth (6th) year, we can use the present value formula.

1. First, we need to determine the present value of the annuity. The formula for calculating the present value of an annuity is PV = P * (1 - (1 + r)^(-n)) / r, where PV is the present value, P is the payment amount, r is the interest rate per period, and n is the number of periods.
2. In this case, the payment amount is $2 million, the interest rate is 8%, and the number of periods is 10 - 6 = 4 (since the payments start at the end of the sixth year).
3. Plugging in these values into the formula, we get: PV = $2 million * (1 - (1 + 0.08)^(-4)) / 0.08 = $5,451,385.89.
4. Therefore, the annual cash flows of the annuity are $5,451,385.89.

Answer 2

$437,946.42

Step-by-step explanation:

Present Value of Deferred Annuity = $2,000,000

Value at the end of Year 5 = $2,000,000*(1.08)^5

Value at the end of Year 5 = $2,938,656.15

Calculation of Annual Payment from Annuity using the TVM

Annual payment = PMT [PV, FV, N, I]

Annual payment = PMT [2,938,656.15, 0, 10, 0.08]

Annual payment = $437,946.42

So, the Annual Payment from annuity is $437,946.42.