find the present value of ordinary annuity
payments of 890 each year for 16 years at 8% compounded annually
What is the amount that must be paid (Present Value) for an annuity with a periodic payment of R dollars to be made at the end of each year for N years, at an interest rate of I% compounded annually?
For this scenario, P = R[1 - (1 + i)^(-n)]/i where P = the Present Value, R = the periodic payment, n = the number of payment periods, and i = I/100.
Example: What is the present value of an annuity that must pay out $12,000 per year for 20 years with an annual interest rate of 6%? Here, R = 12,000, n = 20, and i = .06 resulting in
P = 12000[1 - (1.06)^-20]/.06 = $137,639
Therefore, the purchase of an annuity bearing an annual interest of 6% for $137, 639, will anable the $12,000 annual payment over a 20 year period, for a total payout of $240,000.
Well, let's plug in the values for your specific scenario and calculate the present value of the annuity, shall we?
Given that the periodic payment (R) is $890, the number of payment periods (n) is 16, and the interest rate (I) is 8%, we can calculate the present value (P) using the formula you provided.
First, we need to convert the interest rate to a decimal. So, i = I/100 = 8/100 = 0.08.
Now we can plug in the values:
P = 890[1 - (1 + 0.08)^(-16)]/0.08.
Mmm, let me think. I have an idea to make this process a bit more enjoyable. Let's convert this formula into a mathematical haiku, shall we?
Present Value (P),
Annual payments are bliss,
Math can be funny!
Now, let's continue with the calculations.
P = 890[1 - (1.08)^(-16)]/0.08.
P = 890[1 - 0.315905 ]/0.08.
P = 890 * 0.684095 /0.08.
P = 608.56355.
So, the present value of the annuity is $608.56.
Keep in mind that this is just an estimate, and actual results may vary. But hey, at least we had some mathematical fun along the way, right?
In this case, the periodic payment (R) is $890, the number of payment periods (n) is 16 years, and the interest rate (I) is 8%.
To calculate the Present Value (P), we can use the formula:
P = R[1 - (1 + i)^(-n)]/i
where i is the interest rate divided by 100, so i = 8/100 = 0.08.
Plugging in the values:
P = 890[1 - (1 + 0.08)^(-16)]/0.08
To solve this equation, let's break it down step-by-step:
Step 1: Calculate (1 + 0.08)^(-16):
(1 + 0.08)^(-16) = 0.51359673 (rounded to 8 decimal places)
Step 2: Calculate 1 - (1 + 0.08)^(-16):
1 - 0.51359673 = 0.48640327 (rounded to 8 decimal places)
Step 3: Calculate [890 * (1 - (1 + 0.08)^(-16))]:
890 * 0.48640327 = 434.0579883 (rounded to 8 decimal places)
Step 4: Calculate [890 * (1 - (1 + 0.08)^(-16))] / 0.08:
434.0579883 / 0.08 = 5425.724853 (rounded to 6 decimal places)
Therefore, the present value (P) of the annuity payments is $5425.72.
To find the present value of an ordinary annuity, you need to use the formula P = R[1 - (1 + i)^(-n)]/i. Let's plug in the given values into the formula:
P = 890[1 - (1 + 0.08)^(-16)]/0.08
Now, let's simplify the equation step by step:
Step 1: Calculate the value inside the brackets first:
(1 + 0.08)^(-16) = 0.424103
Step 2: Subtract this value from 1:
1 - 0.424103 = 0.575897
Step 3: Divide this result by the interest rate (0.08):
0.575897 / 0.08 = 7.1987125
Step 4: Finally, multiply this result by the periodic payment (890):
7.1987125 * 890 = 6414.37
Therefore, the present value of the ordinary annuity is $6414.37.