Question

Determine the effective annual yield for each investment. Then select the better investment. Assume 360 days in a year. 9.5% compounded monthly; 9.75% compounded annually. The effective annual yield for a 9.5% compounded monthly investment Round to two decimal places as needed. The effective annual yield for a 9.75% compounded annually investment Round to two decimal places as needed

Answer 1

In order to calculate the final value of the investment, we can use the following equation:

`P=P_0\cdot(1+(r)/(n))^(nt)`

Where P is the final value, P0 is the initial value, r is the annual rate, t is the amount of time and n is a factor relative to the period of compound.

For the first investment, the rate is 9.5 compounded monthly (a year has 12 months, so we use n = 12). So for one year, we have that:

`\begin{gathered} P=P_0(1+(0.095)/(12))^(12) \\ (P)/(P_0)=(1+0.007916667)^(12) \\ (P)/(P_0)=(1.007916667)^(12)=1.09925 \end{gathered}`

The increase in the initial investment is 0.0992 times, that is, 9.92%.

For the second investment, the rate is 9.75% compounded annually (so n = 1), so we have:

`\begin{gathered} P=P_0(1+(0.0975)/(1))^1 \\ (P)/(P_0)=1+(0.0975)/(1)=1.0975 \end{gathered}`

The increase in the initial investment is 0.0975 times, that is, 9.75%.

The first investment has a greater increase in one year, so the first investment is better.