Answer to Question #196929 in Financial Math for Beauty Magadlela

Question

An interest rate of 17,5% per year, compounded quarterly, is equivalent to a continuous compounding rate of

[1] 17,185%.

[2] 17,500%.

[3] 17,128%.

[4] 19,125%.

[5] 17,888%

Answer 1

Continuous compound interest is based on the fact that a division of the rate by n as n approaches infinity is

(1+r/n)ⁿ = e^r (When r=1 this comes to e itself.)

This gives rise to the continuous compound interest formula

A=Pe^rt,

where t is time, r is rate, P is the principal amount and A the amounts after time t. If we take t to be the number of quarters and A/P-1 to represent the rate of interest earned after t quarters, then

e^rt - 1 = e^(0.175/4*4) - 1

=1.191246-1

= 0.191246

=19.125%

Therefore, answer is (4)