A deferred annuity it purchased that will pay and 10000 per quarter for 15 years after being deferred for 5 years .if money is worth 6% annually compounded quarterly what is present value of this annuity?
To find the present value of the deferred annuity, we need to calculate the present value of each quarterly payment and then add them up.
First, we need to find the number of quarterly periods in 15 years:
15 years * 4 quarters per year = 60 quarters
Next, we need to find the future value of each quarterly payment of $10,000 after 60 quarters at a rate of 6% quarterly compounded:
FV = PV * (1 + r)^n
FV = $10,000 * (1 + 0.06/4)^60
FV = $10,000 * 2.74493
FV = $27,449.30
So each quarterly payment has a future value of $27,449.30. But since the payments are being deferred for 5 years, we need to discount each payment back to its present value. Using the formula for present value of a future payment:
PV = FV / (1 + r)^n
PV = $27,449.30 / (1 + 0.06/4)^20
PV = $13,632.44
So each quarterly payment has a present value of $13,632.44. To find the present value of the entire annuity, we simply add up the present value of each quarterly payment:
PV = $13,632.44 * 60
PV = $817,946.40
Therefore, the present value of the deferred annuity is $817,946.40.
Haven't got a clue what the AI is doing ....
Method 1: Pick then end of 5 years as focal point.
Value of annuity at that point
= 10000( 1 - 1.015^-60)/.015
= 393,802.69
Now bring this back to the present time (20 periods)
= 393,802.69(1.015)^-20
= 292,386.85
method2 :
amount of annuity
= 10000(1.015^60 - 1)/.015
= 962,146.52
now bring that back to the present (80 periods)
= 962,146.52(1.015^-80)
= 292,386.85
same answer !!!!! ,
Sorry for the confusion caused earlier. Indeed, the steps you have provided are correct to calculate the present value of the deferred annuity. Method 1 involves finding the present value of the annuity at the end of the 5-year deferral period and then discounting it to the present time, whereas Method 2 involves finding the present value of the entire annuity payment and discounting it to the present time. Both methods lead to the same present value of $292,386.85. Thank you for pointing this out.
To calculate the present value of a deferred annuity, we need to discount the future cash flows back to the present time.
In this case, we have an annuity that pays $10,000 per quarter for 15 years, but it is deferred for 5 years. This means that the first cash flow will occur in 5 years and continue for the next 15 years.
To calculate the present value, we will use the following formula:
PV = C * (1 - (1 + r)^(-n)) / r
Where:
PV is the present value
C is the cash flow per period ($10,000 per quarter)
r is the periodic interest rate (6% annually compounded quarterly, so r = 6% / 4 = 1.5%)
n is the total number of periods (15 years * 4 quarters/year = 60 periods)
Let's plug in the values:
PV = $10,000 * (1 - (1 + 1.5%)^(-60)) / 1.5%
Now, let's calculate the present value using a calculator or spreadsheet:
PV ≈ $359,800.98
Therefore, the present value of this deferred annuity is approximately $359,800.98.