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I am supposed to solve the problem:

A 24-year-old man decides to invest 200,000 euros at a 7% annual interest rate to bring him a regular annual pension from 31 to 50 years inclusive. What will be the pension?

What I did was that I used the formula for the future formula of pension:

$$FV=A\frac{\left ( 1+i \right )^{n}-1}{i}\left ( 1+i \right )=200,000\frac{\left ( 1+0,07 \right )^{7}-1}{0,07}\left ( 1+0,07 \right )=1851960.514$$ and then I divided it for twenty years which is 92598.02

But that is incorrect. The correct solution is 28331.

Can someone tell me, where I made a mistake?

Shelley
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  • One mistake you've made was not accounting for the fact that this man will only start getting his pension at 31.

    From 24 to 30 he will just accumulate interest, meaning his starting principal before starting to take his pension is $200000(1+0.07)^7$ (seven years between 24 and 31). Then you use a formula that as far as I can tell is simply incorrect. You'll want to find the formula for computing the installment. Is there a textbook you're following?

     – Git Gud Oct 27 '19 at 11:31
  • @GitGud I am following the textbook, which is not in english.. but there is written, that if I want final value of pension I should use this formula – Shelley Oct 27 '19 at 11:52
  • The textbook can be wrong, or you may be misinterpreting it. The future value with payments is $P\dfrac{(1+r)^n-1}{r}$ where $P$ is money that the man puts into the investment (not takes out of it), and $n$ is the number of periods and $r$ is the interest rate. It seems to me that you not only picked the wrong formula, the formula you picked is incorrect. I suggest you share a screenshot of the relevant sections of the textbook, maybe someone can help.

    In any case, if you use the correct formula for finding the installments, you'll get the right answer (trust me, I've checked).

     – Git Gud Oct 27 '19 at 12:16
  • @GitGud Can you please tell me the right formula? – Shelley Oct 27 '19 at 12:18
  • I can, but that doesn't help you, you need to find it in your textbook. Ideally you'd learn how to derive it even. The example mentions euros. It's very likely that regular participants here speak your mother tongue. I insist that you share the relevant portions of your textbook. Copy it at your own peril: $A = \dfrac{r P_{0} \left( 1 + r\right)^{n} }{\left(1+r\right)^n - 1}$, where $A$ stands for amortization (the value the man takes out of the pension), $r$ is the interest rate, $n$ is the number of periods and $P_0$ is the starting principal. – Git Gud Oct 27 '19 at 12:23

1 Answers1

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Firstly we need a reference date. I´ve chosen the year when the man is 50 years old. On the LHS the investment is compounded $26$ ($=50-24$) years. On the RHS we use the formula for the geometric series to calculate the future value of $20$ ($=50-31+1$) payments.

$$200,000\cdot 1.07^{26}=x\cdot \frac{1.07^{20}-1}{0.07}$$

$x=...$

callculus42
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