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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

 Feb 22, 2019
 #1
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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".

 Feb 22, 2019

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