Question

Which is most true of an annual rate of 4% compounded quarterly? A) It is equivalent to 4.4% paid annually. B) It is equivalent to 16.99% paid annually. C) It is equivalent to 1% simple interest paid quarterly D) It is equivalent to 4.06% paid annually. Answer: D

Answer 1

Answer:

D) It is equivalent to 4.06% paid annually

Explanation:

Since it is not talking about annuity and simple compound interest, therefore assuming investment value = $100 then interest will be as follows:

Interest for each quarter = $\frac{4}{100} \times \frac{3}{12}$ = 1%

But this 1% will be paid on the compounded value

Interest at end of Quarter 1 = $100 X 1% = $1

Compounded value at end of Quarter 1 = $100 + $1 = $101

Interest at end of Quarter 2 = $101 X 1% = $1.01

Compounded value at end of Quarter 2 = $101 + $1.01 = $102.01

Interest at end of Quarter 3 = $102.01 X 1% = $1.0201

Compounded value at end of Quarter 3 = $102.01 + $1.0201 = $103.0301

Interest at end of Quarter 4 = $103.0301 X 1% = $1.030301

Compounded value at end of Quarter 4 = $103.0301 + $1.030301 = $104.060401

Now net return annually = $4.060401/$100 = 4.06%

Final Answer

D) It is equivalent to 4.06% paid annually