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An investor would like to have £5,000 at the end of 20 years. The annual effective rate of discount is 5%. How much should the investor deposit today to reach that goal?

I tried- PV = FV/(1+i)^t

where Pv= Present value. FV= Future Value. i= rate. and t= time.

PV = 5000/(1+0.05)^20

PV= 1884.447

But this answer is wrong.

Answer = £1,792.43 But how.

What is the difference between annual effective rate of interest and rate of discount?

RajSharma
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1 Answers1

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The rate of discount is $\boxed{d=\frac{i}{1+i}=iv=0.05}$

Now you discount $£ 5,000$ by using the factor $(1-d)$

$PV=£ 5,000\cdot (1-d)^{20}=£ 5,000\cdot (1-0.05)^{20}=£ 1,792.43$

callculus42
  • 30,550
  • Thanks... but I don't understand the difference between annual effective rate of interest and rate of discount? Could you please tell me. – RajSharma Jan 24 '16 at 14:38
  • At the link I tried an explanation. I hope it helps (It should help). http://math.stackexchange.com/questions/1342229/interest-with-inspection-fee-in-promissory-note – callculus42 Jan 25 '16 at 14:35