Optimal Insurance is offering a deferred annuity that promises to pay 10% per annum with equal annual payments beginning at the end of 10 years and continuing for a total of 10 annual payments. For an initial investment of $100,000 what will be the amount of annual payments?** 0-1-2-3-4-5-6-7-8-9-10-11-12-13-14-15-16-17-18-19 $100000? ? ? ? ? ? ? ? ? ? **A) $25,937B) $38,375**C) $42,212**
Answer is C.
Your 100,000 is compounded at 10% for 10 years. 100,000 x (1.1)^10 = 259,374.25
259,374.25 is the present value of your 10-y annuity.
Using BAII N = 10 I=10 PV= -259,374.25 CPT PMT
The answer is C
first you have to draw a time series , so the payement will start at the end of 10th year and countinue equal payments in till the end of 20 ( 10years + 10 annual payments), so first you have to find the FV at the end of 20 year from now, after that take the FV enter it in the calulator , Enter 10 year as N as you want to find the 10 equal payements , Enter 10% as I/Y and PV as 0 ( as you wnat to divide the amount into 10 equal parts so that nothing is there at time 0) the press CPT - PMT , You will get the answer,
Tell me the answer is it correct
Question for cdealbuquerque and Ankit Sharma:
How can you assume the discount rate is the same as the annuity payout rate (i.e., 10%). If you had alternative investments with higher rates and equivilent risk, wouldn’t you use that discount rate?
Very interesting point. The discount rate is the annuity payout rate unless another rate is given.
There is no way to solve the problem without making this assumption.
Fully satisfied by cdealbuquerque
Shouldn’t it be B? 100000 x (1.1)^9 = A x ((1- (1/(1.1^10)))/0.1) => A = 38374.51 Since annuity begins at end of 10 years, we should use PV at end of 9 years.
I’m gettting C as well. If you draw out the timeline, you’ll see that the annuity payments start at the end of year 10 which is equal to the beginning of year 11. Since you are at the start of Year 0 now and will be buying the annuity at the beginning of year 10, you compound for ten years. You then get to wait one year for the annuity to start paying out.
Good catch though that annuities are priced as of the year before they start paying out; just in this situation, I think the wording of the problem already factors that in.
In a nutshell, you leave money on deposit with Optimal Insurance that rolls up with 10% interest for a full 10 years, at which point you receive your first payment and each year thereafter for 9 more years.
To solve, you can use either the 10 year accumulated balance of $259,374.25 and solve using an annuity due for 10 years or the approach self_employed has used with the 9 year accumulated balance and using an immediate annuity. Both ways should give you $38,375.
1.draw timeline and you will see that u have to deal with TVM only not C/F method because u don’t know the cash flow of Y11-Y20, even u know CF0, CF1-10 = 0 , discounted rate.
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push BA II by these sequences : 10 N, 10 I/Y,100,000 +/- PV, 0 PMT,CPT,FV then u got FV = 259,374.25
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now u move your timeframe to ending of Year10 already then start calculate the payment with the beginning mode.
4.continually push BA II: 259,374.25 PV and 0 FV with the same value in I/Y and N, then CPT PMT = -38,374.51, that are the amount that they will pay u, base on today.
the approach self_employed has used with the 9 year accumulated balance and using an immediate annuity
how to do like that, would u mind to show the calculator sequence?
Set P/Y = C/Y =1 and payments to END.
N=10, I=10%, PV =-235,794.77, CPT PMT
PMT is 38,374.51