Question

The assets of Potential Corp. grew from 2.3 to 3.3 million dollars in just nine months. What return was earned over the nine month period? What was the monthly return assuming monthly compounding? What was the APR? What was the EAR?

Answer 1

Holding period return = (End value – Initial value) /Initial value

                                        = ($ 3,300,000 – $ 2,300,000)/ $ 2,300,000

                                        = $ 1,000,000/$ 2,300,000 = 0.434782609 or 43.48 %

Return of 43.48 % was earned over nine month of period.

Monthly return = (Holding-period return + 1)^1/t – 1

                             = (0.434782609 + 1)^1/9 – 1

                             = (1. 434782609) ^0.111111111 – 1

                             = 1.04092797 – 1

                            = 0.04092797 or 4.09 %

Monthly return assuming monthly compounding is 4.09 %

APR = Monthly return x 12 = 0.04092797 x 12 = 0.491135637 or 49.11 %

APR was 49.11 %

EAR = (1 + APR/n) ⁿ – 1

       = (1 + 0.491135637/12) ¹² – 1

       = (1 + 0.04092797) ¹² – 1

        = (1.04092797) ¹² – 1

        = 1.6182594 – 1

        = 0.6182594 or 61.83 %

APR was 61.83 %