Find the APR, or stated rate, in each of the following cases (Do not round intermediate
calculations and enter your answers as a percent rounded to 2 decimal places, e.g.,
32.16.):
Stated Rate (APR)
Number of Times Compounded
Effective Rate (EAR)
%
Semiannually
11.1 %
Monthly
19.6
Weekly
10.5
Infinite
8.4

Respuesta :

Based on the given rates, the APR for each period of compounding is:

  • Semiannually 11.1 % = 10.8%
  • Monthly 19.6% = 18.03%
  • Weekly 10.5% = 9.99%
  • Infinite 8.4% = 8.07%

What are the APRs?

The semiannual APR is:

= ( (1 + rate) ^ 1/ compounding periods - 1) x 2

= ( (1 + 11.1%) ¹/² - 1) x 2

= 10.8%

The monthly rate:

= ( (1 + 19.6%)  ¹/ ¹²) - 1) * 12

= 18.03%

The weekly rate:

= ( (1 + 10.5%)  ¹/ ⁵²) - 1) * 52

= 9.99%

The infinite rate:

= (Log (1 + rate)) / Loge

= Log (1 + 8.4%) / Log e

= 8.07%

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