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Chapter 5: Q.38 (page 324)

What rate of interest compounded continuously will yield an effective interest rate of 6%?

Short Answer

Expert verified

The rate of interest that when compounded continuously will yield an effective interest rate of 6% is 5.827%

Step by step solution

01

Step 1. Given Information

Given to determine the rate of interest that when compounded continuously will yield an effective interest rate of 6%

02

Step 2. Calculation

The effective rate of interest r_e for an investment with rate of interest r and compounded continuously is given by $r_{e} = e^{r} - 1$

Here the effective rate of interest is 6%, the decimal form is given by $r_{e} = 0.06$

Plugging the values:

$r_{e} = e^{r} - 1 0.06 = e^{r} - 1 e^{r} = 0.06 + 1 e^{r} = 1.06 r = \ln (1.06) r = 0.058268$

03

Step 3. Conclusion

The rate of interest that when compounded continuously will yield an effective interest rate of 6% is 5.827%

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Most popular questions from this chapter

Begin with the graph of $y = e^{x}$ and use transformation to graph the function. Determine the domain, range and horizontal asymptote of the function.

$f (x) = e^{x + 2}$

Height and Head Circumference. The head circumference

C of a child is related to the height H of the child (both in inches) through the function $H (C) = 2.15 C - 10.53$

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(b) Verify that $C = C (H)$ is the inverse of $H = H (C)$ by showing that $H (C (H)) = H$ and $C (H (C)) = C$ .

(c) Predict the head circumference of a child who is $26$ inches tall.

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Evaluate each expression using the graphs of $y = f (x)$ and $y = g (x)$ shown in the figure.

(a) $(g \circ f) (- 1)$ (b) $(g \circ f) (0)$ (c) $(f \circ g) (- 1)$ (d) $(f \circ g) (4)$ .

If $2^{x} = 3$ , what does $4^{- x}$ equal?

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