To compare investments, analysts convert monthly, quarterly, and semiannual rates to annual rates. If an investment of $100,000 is invested at 3.5% per quarter, compounded quarterly, the growth can be modeled by the equation A(t) = 100,000(1.035)4t. What is the equivalent annual growth rate for this investment (rounded to the nearest hundredth of a percent) and what is it worth (rounded to the nearest thousand dollar) after 15 years?
A.) 0.32% and $104,000
B.) 14.75% and $788,00
C.) 10.50% and $447,000
D.) 14.01% and $714,000
I believe it is b :(?
A(t) = 100,000(1.035)4t.
(1.035)^4=1.147523000625 - 1 =.1475 X 100=14.75% Effective annual rate.
A(t)=100,000(1.035)^4*15
A(t)=100,000(1.035)^60
A(t)=100,000 X 7.8780909....
A(t)=$787,809.09 FV of $100,000 @ 3.5% per quarter compounded quarterly.
From the answers above, it can be seen that the answer is B
