Question

Two investments: one compounded continously, other is monthly.

Monthly Rate: Stated rate is 6.5%

Comp cont ? <- what is this rate (Must make both returns equal eachother)

Answer 1

We know quoted rate is quoted rate for monthly compounding = 6.5%

Effective rate = (1+Rate/12)^12-1 = (1+6.5%/12)^12-1 = 6.697185%

Now, we should get same rate when we used continuous compounding by using below:

exponential “e” is used for continuous compounding result;

Target rate = 6.697185%

Now:

Target Rate = e^r - 1

6.697185% = e^r - 1

e^r = 1+6.697185%

Applying natural log on both the side:

r x ln(e) = ln(1.06697185)

Note: ln(e) = 1

r x 1 = 0.06482459

r = 6.482459%

Hence, quoted rate for continuously compounding will be 6.482459% or ~6.4824%