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?
The rate of discount is $\boxed{d=\frac{i}{1+i}=iv=0.05}$
Now you discount $£ 5,000$ by using the factor $(1-d)$
$PV=£ 5,000\cdot (1-d)^{20}=£ 5,000\cdot (1-0.05)^{20}=£ 1,792.43$