Question $1(3$ points$)$

Which of the following statements are false?

The cash flows on an annuity due occur at the beginning of each period.

Nominal interest rates are the interest rates we observe in the market.

The rule of $72$ can be used to tell approximately how long it will take an annuity's value to double.

If you can earn $8\%$ on an investment it will double in approximately $9$ years.

Statement one $(1)$ is false.

Statement two $(2)$ is false.

Statement three $(3)$ is false.

Statement four $(4)$ is false.

Question $2(3$ points$)$

Which of the following statements are false?

An annuity is a series of equal cash flows, or payments, made at regular intervals.

For a discount loan interest is deducted upfront from the loan proceeds.

If inflation expectations increase we would expect nominal interest rates to rise.

The present value of a lump sum increases with the frequency of compounding.

Statement one $(1)$ is false.

Statement two $(2)$ is false.

Statement three $(3)$ is false.

Statement four $(4)$ is false.