Answer to Question #311083 in Financial Math for tumi

Question

An interest rate of 14,90% per year, compounded every 3 months, is equivalent to a weekly compounded interest rate of

Answer 1

A=P(1+r/n)^nt

Assume we have a principle of 50000, which is to be compounded over a ten year period

=50000(1+14.9%/4)⁴⁰

=50000(1.03725)⁴⁰

=50000(4.3185)

=215925

So we now are going to compute the rate of interest that is required to compound 50000 into 215925 over a ten year period.

215925=50000(1+r/52)⁵²⁰

215925/50000=(1+r/52)⁵²⁰

4.3185=(1+r/52)⁵²⁰

We now find the 520th root on both sides to get the below equation

1.002817=1+r/52

Solving it we find that the rate is 14.65%

R=14.65%

So the correct answer is 14.65%