Continuous Compounding

[mroberts]

a) A bank quotes an interest rate of 6%, compounded continuously. Find the equivalent rate with annual compounding.

Here's my attempt.

I have used a Present value of 1,000 and a 5 year time period.Continuous Compounding
FV = PV x e^(r x n)
FV = PV x e^(0.06x5)
FV = 1,000e^(0.06x5)
1,349.86
Annual Compounding (solving for i)
FV = PV (1+i)^n
1,349.86 = 1,000(1+i)^5
1.35… = (1+i)^5
5√1.35...= 1+i
I = 0.0618 or 6.18%
The equivalent rate with annual compounding is 6.18%

Can i have your opinion please?
Regards
Marshall

 

[Deleted member 4993]

a) A bank quotes an interest rate of 6%, compounded continuously. Find the equivalent rate with annual compounding.

Here's my attempt.

I have used a Present value of 1,000 and a 5 year time period.Continuous Compounding
FV = PV x e^(r x n)
FV = PV x e^(0.06x5)
FV = 1,000e^(0.06x5)
1,349.86
Annual Compounding (solving for i)
FV = PV (1+i)^n
1,349.86 = 1,000(1+i)^5
1.35… = (1+i)^5
5√1.35...= 1+i
I = 0.0618 or 6.18%
The equivalent rate with annual compounding is 6.18%

Can i have your opinion please?
Regards
Marshall

Why did you choose n=5? Would the answer be same if n= 10? or n= 0.5?

By the way, numerical value is correct.

Prove it by for a generic 'n'!

 

[DexterOnline]

\(\displaystyle i=e^{0.06}-1\)

\(\displaystyle i=2.7182818284590452353602874713527^{0.06}-1\)

\(\displaystyle i=1.0618365465453596222246848771684-1\)

\(\displaystyle i=0.0618365465453596222246848771684\)

\(\displaystyle i=6.18\%\)

 

[jonah2.0]

Beer soaked ramblings follow.

Ah Sir Dexter, 'tis indeed good to hear from thou again.
I take it thy online business is going well?