You were offered the opportunity to purchase either a simple interest note or a simple discount note with the following terms: $33,353 at 7% for 18 months.


a.
Calculate the effective interest rate. (Do not round intermediate calculations. Round your final answer to the nearest tenth percent.)

Effective interest rate



b. Based on the effective interest rate, which would you choose?


simple interest note
simple discount note

Simple interest note

To calculate the effective interest rate, we need to first calculate the interest amount for both the simple interest note and the simple discount note, and then compare them.

For the simple interest note:
Principal amount (P) = $33,353
Interest rate (r) = 7% per year
Time (t) = 18 months = 1.5 years

Using the simple interest formula: Interest = P * r * t
Interest = $33,353 * 0.07 * 1.5 = $3,498.82

For the simple discount note:
Principal amount (P) = $33,353
Discount rate (r) = ?
Time (t) = 18 months = 1.5 years

Using the simple discount formula: Discount = P * r * t
Discount = $33,353 * r * 1.5

Now, we need to equate the discount amount to the interest amount:
$33,353 * r * 1.5 = $3,498.82

Solving for r:
r = $3,498.82 / ($33,353 * 1.5)
r ≈ 0.021

The effective interest rate is approximately 0.021 or 2.1%.

To determine which option to choose based on the effective interest rate, we compare it to the prevailing interest rates in the market for similar types of investments. If the effective interest rate is higher than the prevailing rates, then the simple interest note would be the better choice. On the other hand, if the effective interest rate is lower, then the simple discount note would be preferable.

Evelyn saved $ 1000 at the end of every six months for five years in a savings account earned 4% compounded semi-annually. At the end of the five years, she let her money compound at 6% compounded quarterly for the next five years. Calculate the balance in her savings account at the end of 10 years and the total interest earned over this term.

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