In order to compare investments, analysts will convert monthly, quarterly, semi-annual rates to annual rates.
If an investment of $100,000 is invested at 1.5% per month compounded monthly, the growth can be modeled by the equation:
A(t)=100,000(1.015)^12t
What is the equivalent annual growth rate for this investment (rounded to the nearest tenth of a percent) and what is it worth (rounded to the nearest whole dollar) after 15 years?
Select one:
a. 19.6%, and $1,458,437
b. 15.0% and $813,706
c. 25.1% and $2,876,467
d. 12.0% and $547,357
1) Interest rate conversion:
Effective annual rate =[1 + 1.5%]^12
=[1 + 0.015]^12
=[1.015]^12
=1.19561817... - 1 x 100
=~19.6% - effective annual rate.
2) FV =PV x [1 + R]^N
=PV x [1 + 1.5%]^(15*12)
=$100,000 x [1.015]^180
=$100,000 x 14.58436768913............
=$1,458,437 - Growth in this investment after 15 year @ 1.5% comp.monthly
The answer is "a".
