accumulation factors and interest rates

[Sashoye]

Hi All,

I hope someone could help me to understand what is happening here with this example.

EXAMPLE:

Given that: A(t,t+h)=1+hi_{h ,}

where CA(t_1,t₂) is an accumulation factor of an investment C.

If we invest £80 at time 5 and the accumulated amount at time 8 is £100.

A(5,8)=100/80=1.25 AND i₃(5)=(1.25 -1)/3=8.33%

If the time above is in years, what is the effective annual interest rate?

I can see the answer from the notes is 1.25^{1/3 -}1=7.72% But I don't fully understand WHY.

Could someone explain why?

Thanks in advance

 

[Sashoye]

80 increases to 100 over 3 years; i = interest rate:
80(1 + i)^3 = 100
(1 + i)^3 = 100/80 = 1.25
1 + i = 1.25^(1/3)
i = 1.25^(1/3) - 1
i = 1.0772 - 1
i = .0772 which is 7.72%

That is basic stuff that you should know.
Look up "future value" financial formulas.

Anyway, if that is what you're learning,
then the problem is BADLY worded;
could simply be:

80 is deposited now, and grows to 100 over 3 years;
what is the annual interest rate?

NOTHING else is required...tell your teacher!

Thanks for your help. I did eventually figure it out. Yes, I agree the question/ example is badly worded.