Question

Please show all your work for the following question. answer with PV, FV, PMT, IY, and N butfons for financial calculators if possible.

3. A) For a deposit, what APR compounded quarterly will produce the same effective annual rate as 12% APR compounded weekly? B) For a deposit, what APR compounded semi-annually will produce the same effective annual rate as 12% APR compounded monthly?

Answer 1

3 A) 12% APR compounded weekly

Step 1: Effective weekly interest rate = 12%/52 = 0.002307692308

Step 2: Effective quarterly rate.

There are 3 * 4 = 12 weeks in a quarter

Effective quarterly rate = (1 + 0.002307692308)^12 - 1

Effective quarterly rate = 0.02804650476

Step 3: APR compounded quarterly = 0.02804650476 * 4

APR compounded quarterly = 0.112186019

APR compounded quarterly = 11.2186019%

B) 12% APR compounded monthly

Step 1: Effective monthly rate = 12%/12 = 0.01

Step 2: Effective semi-annual rate = (1 + 0.01)^6 - 1

Effective semi-annual rate = 0.0615201506

Effective semi-annual rate = 6.15201506%

Step 3: APR compounded semi-annual rate = 0.0615201506 * 2

APR compounded semi-annual rate = 0.1230403012

APR compounded semi-annual rate = 12.30403012%

(Note it is not possible to find the APR rates directly using the TVM keys)

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