Tabansi

2021-08-12

Find the effective interest rate $r}_{e$ for investments with the following annual interest rates.

Express your answer as a percentage, rounded to 2 decimals, and without the$}$ sign (e.g., 8.79)

a)$3.55\mathrm{\%}$ compounded monthly

b)$3.53\mathrm{\%}$ compounded daily (using 365 days per year).

c)$3.49\mathrm{\%}$ compounded continuously

Express your answer as a percentage, rounded to 2 decimals, and without the

a)

b)

c)

Tuthornt

Skilled2021-08-13Added 107 answers

Step 1

Here we have to find the effective interest rate for investment with the following interest rate,

So, we will use the following formula,

${r}_{e}={(1+\frac{r}{n})}^{n}-1$

Or,${r}_{e}={e}^{r}-1$

Here it is depending on if the interest is compounded n times per year or continuously.

Step 2

a)$3.55\mathrm{\%}$ compounded monthly

So, here we use the formula,${r}_{e}={(1-\frac{r}{n})}^{n}-1$

Where,$r=0.0355$ and $n=12$

So,${r}_{e}={(1+\frac{0.0355}{12})}^{12}-1$

${r}_{e}={\left(1.002958\right)}^{12}-1$

${r}_{e}=0.03608$

Hence, the effective interest rate is about$3.61\mathrm{\%}$

Step 3

b)$3.53\mathrm{\%}$ compounded daily (using 365 days per year).

Using the formula,${r}_{e}={(1+\frac{r}{n})}^{n}-1$

Where,$r=0.0353$ and $n=365$

So,${r}_{e}={(1+\frac{0.0353}{365})}^{365}-1$

${r}_{e}=0.03592$

Hence, the effective interest rate is about$3.59\mathrm{\%}$

Step 4

c)$3.49\mathrm{\%}$ compounded continuously

Here, we are using the formula${r}_{e}={e}^{r}-1$

Where,$r=0.0349$

${r}_{e}={e}^{0.0349}-1$

${r}_{e}=0.03551$

Hence, the effective interest rate is about$3.55\mathrm{\%}$

Here we have to find the effective interest rate for investment with the following interest rate,

So, we will use the following formula,

Or,

Here it is depending on if the interest is compounded n times per year or continuously.

Step 2

a)

So, here we use the formula,

Where,

So,

Hence, the effective interest rate is about

Step 3

b)

Using the formula,

Where,

So,

Hence, the effective interest rate is about

Step 4

c)

Here, we are using the formula

Where,

Hence, the effective interest rate is about

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