Question

Bank D pays 7.289% effective annual yield on an investment account in which interest is compounded weekly. What is the annual interest rate before compounding? Enter your answer as a percent, rounded to the nearest four decimals, without the % sign, (9.34562% should be input as 9.3456.)

Answer 1

Answer:

7.0403

Explanation:

Suppose the initial investment is $1, we start the formula rEFF=A−P0P0. Next, substituting, we now have 0.07289=A−11 or 0.07289=A−1, so A=$1.07289. We now use this value for A in the formula A=P0⋅(1+rk)N⋅k with P0=$1, k=52 compounding periods for weekly compounded interest, N=1 year, and r is the unknown monthly compounded interest rate for which we are solving. Plug the values into the formula. Take the fifty-second root of both sides. Next, subtract 1 from both sides, and multiply both sides by 52.

1.072891.00135390.00135390.0704028=(1+r52)52=1+r52=r52=r

The final step gives us 0.0704028, converted into a percentage and rounded to four decimal places is 7.0403.

Answer 2

Answer:

annual percentage rate: 7.0404%

Explanation:

We need to solve for the annual convertible rate  when we are given with the annual effective rate:

$(1+APR/52)^{52}=1+0.07289\\APR =( \sqrt[52]{1.07289} -1) \times 52$

apr = 0.0704035593 = 7.0404%