Question

Today, you borrowed $20,000 at 5.5% with quarterly compounding. You have agreed to pay off the loan over 5 years by making equal weekly payments. If you were solving for your unknown weekly payment amount using the annuity present value equation, what interest rate would you use? (Hint: You don't actually need to solve for your unknown payment amount.) Do not round intermediate calculations. Round the final answer to 2 decimal places. Omit the % sign in your response. For example, an answer of 15.39% should be entered as 15.39

Answer 1

Rate to be used 0.42

The Weekly payment amount need not be solved,

Only the Interest rate that would be used to arrive at the weekly payment is required.

The given rate is 5.5% compounded quarterly

if quarterly rate is 5.5%, the corresponding yearly rate is 22% ( 5.5 X   4 quarters in a year)

Since payments are weekly- we need a weekly interest rate

if yearly rate is 22%, the corresponding weekly rate is 0.423076923% ( 22 / 52 weeks in a year)

Alternatively,

if quarterly rate is 5.5%, the corresponding weekly rate is 0.423076923% ( 5.5 / 13 weeks in a quarter)