Need help with an annuity question? - american general annuity
American General has a 7-years with an annual regular guaranteed rate of 6.35%. How much should you pay for these pensions in the amount of $ 10,000 per year over the next 7 years will receive?
American General Annuity Need Help With An Annuity Question?
2 comments:
Nick has the right answer: It is indeed at U.S. $ 55,135.98. The second hypothesis
seems correct to say that the pension will be general information offered by the American insurance or any other office, expects that the principal sum is exhausted. The reason why I am saying is that pensions are the type of financial institution, that these companies are generally the business in the deployment. The annual payment exceeds that are of interest, is a blend of principal and interest.
What they demand is less than the present value of fixed income since the interest rate, maturity and payment of the annual amount that you have specified. When Nick is also given for this trial and error methods, then I say he deserves because he has done, must be an awful big help.
But I think you'll be glad to know that there is a formula for dealing with ease and simplicity are. With him I could result in a split second, the use of Microsoft Excel, after writing the requiredssary formula. I show that the formula and explain how I hope your current needs and demands of you. I hope that Nick will benefit from it, even as he has shown an interest in nature.
The formula is:
P = (A / I) * [(1 + i) ^ n - 1] / [(1 + i) ^ n], where
P = principal amount;
A = annual sum to be paid;
i = interest rate, are issued annually, and
n = time in years.
But if you wanted an explanation of the formula is this:
The formula is based on the mathematical formula for the sum of a geometric series, namely, S = 1 + x + x + x ² + ³ ... based + X ^ (n - 1) = (x ^ n - 1) / (x - 1).
You can check by multiplying the series term by term, look for x - 1; that by deleting all the intermediate conditions is easily obtained, then multiply the result of x ^ n - 1
Well, if you let x = 1 + i, we obtain
S = [(1 + i) ^ n - 1] / I.
This is s, the amount with interest at the end of the yearYears, by the deposit of one dollar or pound or other currency at the end of each of n years.
On the other hand, if you make a deposit, a deposit is not repeated, for $ 1 or £ 1 and had it for years n to collect, with interest to see that you
G = (1 + i) ^ n,
accumulated at the end of the day.
In a third case, suppose you wanted to know how much the file is now once again a single stock, up to $ 1 until the end of the year s earning year.
The deposit is 1 / G = 1 / (1 + i) ^ n
This is how the current value of 1, N end known: you pay 1 / G now, and you have 1 at the end of the period of n years. 1 / G is known as the present value of 1.
So, what is the present value of an agreed rent for a period of n years? In other words, you pay a lump sum now and win (like a bank, the collection of a loan) the amount at the end of each of n years. What is the present value of the S? If the annual amount is $ 1, then we have:
P = S / G = (1 / i) * [(1 + i) ^ n - 1] / [(1 + i) ^ n];
but as the annual amount of A, which multiply not necessarily 1, the amount of one and get:
P = (A / I) * [(1 + i) ^ n - 1] / [(1 + i) ^ n].
Now, using the above formula and values
i = 0.0635, n = 7 and A = 10000
Calculator give you the results of 55,135.98, shown above.
He writes in Excel, you can take care if you try to have Excel.
Below again is what I got back:
.0635
7
10000
Power = ((1 + a1) a2) (in the language, Excel, Central 1.0635 ^ 7)
= (A4-1) / A1
= A5/A4
A6 = A3 *
0.0635
7
10000
1.538730137 give (G)
8.483939158 (S) This gives
5.513597841 (the current value of S)
55135.97841 (in the A multiplied in order to get P)
I hope this answer is helpful.
The payments are accrued interest. How do we want the annual payments, the annual interest to work. The interest rate is 6.35% in this case. Is the time that a period of activity will be paid before interest that one years in this case. The amount of rent paid is the main thing is what we find.
Interest = principal x rate x time
We are the most important penalty that
Interest = principal (rate) x time
The interest is $ 10,000
The price is 6.35% per year = 0.0635 / y
Time = 1 years
Hence Principal = $ 10,000 / (0.0635 x 1) = $ 157,480.31. This is the amount up to $ 10,000 per year to make, without loss of principal.
If, however, it will reduce the director, to more than seven years to zero, the problem is completely different. I've never had such problems, but worked through trial and error and came up with an initial payment of $ 55,136.00. I http://www.moneychimp.com/calculator/ann the simulator ... Sorry, I do not know how to reach the mathematicsal.
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