Q.37 What rate of interest compounded... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 5: Q.37 (page 324)

What rate of interest compounded quarterly will yield an effective interest rate of 7%?

Short Answer

Expert verified

The rate of interest that when compounded quarterly will yield an effective interest rate of 7% is 6.823%

Step by step solution

Step 1. Given Information

Given to determine the rate of interest that when compounded quarterly will yield an effective interest rate of 7%

Step 2. Calculation

The effective rate of interest r_e for an investment with rate of interest r and compounding n times per year is given by $r_{e} = {(1 + \frac{r}{n})}^{n} - 1$

Here the investment is compounded quarterly. So $n = 4$

And since the effective rate of interest is 7%, the decimal form is given by role="math" localid="1646650286759" $r_{e} = 0.07$

Plugging the values:

role="math" localid="1646650531814" $r_{e} = {(1 + \frac{r}{n})}^{n} - 1 0.07 = {(1 + \frac{r}{4})}^{4} - 1 {(1 + \frac{r}{4})}^{4} = 0.07 + 1 {(1 + \frac{r}{4})}^{4} = 1.07 1 + \frac{r}{4} = \sqrt[4]{1.07} 1 + \frac{r}{4} 鈮� 1.017058 \frac{r}{4} = 1.017058 - 1 \frac{r}{4} = 0.017058 r = 0.06823$

Step 3. Conclusion

The rate of interest that when compounded quarterly will yield an effective interest rate of 7% is 6.823%

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91影视

What rate of interest compounded quarterly will yield an effective interest rate of 7%?

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

Step 3. Conclusion

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