# Thread: Deferred Annuity problem

1. ## Deferred Annuity problem

I need help answering this problem:

A sequence of 8 annual payments of $750 each, with the first payment due at the beginning of the 6th year; money is worth 6%. (The beginning of year 6 is the end of year 5.) Find the present value. This is my answer: 750 [ (1-1.06^-13) / .06 ] - 750 [ (1-1.06^-5) / .06 ] =$3,480.24

that'll give you a present value (loan proceeds) of $4,657. Now just get present value of that today: 4657 / 1.06^4 = 3689 9. ## Re: Deferred Annuity problem My attachment shows this method, except for the payments. 10. ## Re: Deferred Annuity problem It looks like you're using the formula for an annuity immediate (when interest is applied at the end of the year), rather than for an annuity due (when interest is applied at the beginning of the year). The formula should be $\"{a}_{n,i}=\frac{1-\frac{1}{1+i}^{n}}{\frac{i}{1+i}}$ So, what you typed should look like this: 750 [[ (1-1.06^-13) / .06 ]/1.06] - 750 [[ (1-1.06^-5) / .06 ]/1.06]=3,689.0544 I hope that helps. 11. ## Re: Deferred Annuity problem I took a different approach to a solution: I used Excel and created a simple timeline of 12 periods, populating zero into the first four, and 750 in periods five through twelve, thus representing four time-periods with zero payments, followed by eight with$750.

I then used the NPV function with a 6% rate, and the stream of cash flows (Note: with the first 750 entered in period 5, this is assuming payment at the END of the 5th period {or the beginning of #6})

The NPV evaluates to \$3,689.05; the same as the text book.

To Amul28's comment about Euros vs Dollars, it wouldn't matter as long as the same units are used throughout...

12. ## Re: Deferred Annuity problem

FYI, copying and pasting that formula into Wolfram Alpha results in a valuation of 3,283.24

Originally Posted by downthesun01
The formula should be

$\"{a}_{n,i}=\frac{1-\frac{1}{1+i}^{n}}{\frac{i}{1+i}}$

So, what you typed should look like this:

750 [[ (1-1.06^-13) / .06 ]/1.06] - 750 [[ (1-1.06^-5) / .06 ]/1.06]=3,689.0544

13. ## Re: Deferred Annuity problem

I need help answering this problem:

A sequence of 8 annual payments of 750 each, with the first payment due at the beginning of the 6th year; money is worth 6%.

(The beginning of year 6 is the end of year 5.) Find the present value.

This is my answer: 750 [ (1-1.06^-13) / .06 ] - 750 [ (1-1.06^-5) / .06 ] = 3,480.24

and this is the book's: 3,689 .

The book didn't provide a solution, so I would really appreciate it if someone can help me find where my solution went

wrong. Thank you!
Present value formula
Code:
PV = R . (1+i*type) . (1+i)^-d [ 1 - (1+i)^-n ] / i
where

R = annuity payment
i = interest rate
type = 0 for end of period payments, 1 for start of period payments
d = time period by which annuity is deferred
n = total number of payments

Your problem has the following data

Code:
PV = R . (1+i*type) . (1+i)^-d [ 1 - (1+i)^-n ] / i

R = 750
i = 6% = 0.06
type = 1 for start of period annuity
d = 5 as the first payment is deferred by 5 periods
n = 8 as there are 8 annuity payments

750 (1+6%)^-5 (1+6%) [ 1-(1+6%)^-8 ] / 6%
750 (1+0.06)^-5 (1+0.06) [ 1-(1+0.06)^-8 ] / 0.06
750 (1.06)^-5 (1.06) [ 1-(1.06)^-8 ] / 0.06
750 (0.74725817286605716719189988974845) (1.06) [ 1-0.62741237134182678250493686881491 ] / 0.06
750 (0.74725817286605716719189988974845) (1.06) [ 0.37258762865817321749506313118509 ] / 0.06
750 (0.74725817286605716719189988974845) (1.06) (6.2097938109695536249177188530833)
750 (0.74725817286605716719189988974845) (6.5823814396277268424127819842683)
750 (4.9187383276836621437572364513326)
PV = 3689.05

14. ## Re: Deferred Annuity problem

WHY re-activate a 2 years old inactive thread?

15. ## Re: Deferred Annuity problem

Originally Posted by Wilmer
WHY re-activate a 2 years old inactive thread?
Hello Wilmer

I only found the thread on the second page of the forum, thus overlooked the date and assumed it must be from recent months

BTW, is there a restriction of invoking older threads?

Do they just bury the dead. I thought Thy Lord had the powers to resurrect the dead to life.

I had assumed the formula I presented will help out those seeking present value of a deferred annuity

If you think I had erred on judgement, then let Thy Lord be a witness that I shall not make the same mistake twice

But then I tend to forget things

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