Suppose you have a choice of two equally risky annuities, each paying $1,000 per year for 20 years with similar interest rates. One is an annuity due, while the other is an ordinary annuity. Which annuity would you choose

Annuity due would be be chosen.

Explanation:

Let us assume the similar annual interest rate is 10%.

To decide which to choose, the present values of the two annuities are calculated and compared as follows:

1. For annuity due

Under an annuity due, payments are made to investors at the beginning of each time period. The present value of an annuity due can be calculated as follows:

PVd = P × [{1 - [1 ÷ (1+r)]^n} ÷ r] × (1+r) (1)

Where;

PVd = Present value of an annuity due = ?

P = Annual payment = $1,000

r = interest rate = 10%, or 0.10

n = number of years = 20

Substituting the values into equation (1) above, we have:

PVd = $1,000 × [{1 - [1 ÷ (1 + 0.10)]^20} ÷ 0.10] × (1 + 0.10) = $9,364.92

2. For ordinary annuity

Under an ordinary annuity, payments are made to investors at the end of each time period. The present value of an ordinary annuity can be calculated as follows:

PVd = P × [{1 - [1 ÷ (1+r)]^n} ÷ r] (2)

Where

PVo = Present value of an ordinary annuity = ?

P = Annual payment = $1,000

r = interest rate = 10%, or 0.10

n = number of years = 20

Substituting the values into equation (1) above, we have:

PVo = $1,000 × [{1 - [1 ÷ (1 + 0.10)]^20} ÷ 0.10] = $8,513.56

3. Decision

Since the present value (PV) of the annuity due of $9,364.92 is greater than the PV of ordinary annuity of $8,513.56, annuity due would be be chosen.

i believe the answer would have to be a dependable person

of the three mortgage options that demarco and tanya have to choose from, the balloon payment mortgage would be their best option, over adjustable payment and fixed payment plans.ultimately, the balloon payment plan would save demarco and tanya overall, in interest, would cost less monthly, and they would only have to make these payments for 8 years, opposing to 30 years for adjustable or fixed payment plans. 

overall, demarco and tanya would save $80,811 if they chose balloon payments over fixed payments, and would save $116,711 if they choose balloon payments over adjustable payments. benefits with choosing fixed payments over adjustable payments is that, in the end, the payments will still be $836.30 a month, while with adjustable payments, the initial monthly payments will be $763.38 to $1082.70 a month, ultimately leading to a more costly purchase. benefits with choosing fixed payments over balloon payments are not present. benefits in choosing adjustable payments over is that it has a lower interest rate, and starts with lower monthly payments initially. benefits in choosing adjustable payments over balloon payments include a lower interest rate, and lower initial monthly payments. benefits in choosing balloon payments over fixed payments include lower interest rates, lower overall price, lower monthly payments, takes less time to pay off, and does not require a downpayment. benefits in choosing balloon payments over adjustable payments include, lower monthly payments (when averaged), takes less time to pay off, and lower overall price.

hence, option c, balloon payments, is the best option for demarco and tanya to make this purchase, for it will save them a minimum of $80811, and a maximum of $116,711.