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Chapter 5: Q. 19 (page 324)

Find the principal needed now to get each amount; that is, find the present value to get $600 after 2 years at 4% compounded quarterly.

Short Answer

Expert verified

The answer is $554.09

Step by step solution

01

Step 1. Given information

The amount, $A = $ 600$

The rate of interest, $r = 4 % = \frac{4}{100} = 0.04$

The time period, $t = 2 y e a r s$

The investment compounded quarterly, $n = 4$

02

Step 2. Use Present value formulas

The present value P of A dollars received after t years, assuming a per annum interest rate r compounded n times per year, is $P = A {(1 + \frac{r}{n})}^{- n t}$

03

Step 3. Calculation

Substitute the values in the Present value formula,

$P = $ 600 {(1 + \frac{0.04}{4})}^{- (4 \times 2)} P = $ 600 {(1.01)}^{- 8} P = $ 600 {(0.990099)}^{8} P = $ 600 (0.92348) P = $ 554.09$

The Present value, $P = $ 554.09$

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Most popular questions from this chapter

In Problems $33 - 40$ , the graph of an exponential function is given. Match each graph to one of the following functions.

The graph of an exponential function is given. Match each graph to one of the following functions.

As the base a of an exponential function $f (x) = a^{x}$ , where $a > 1$ increases, what happens to the behavior of its graph for $x > o ?$ What happens to the behavior of its graph for $x < 0 ?$

the function f is one-to-one. Find its inverse and check your answer.

$f (x) = \frac{x^{2} + 3}{3 x^{2}} x > 0$

The domain of a one-to-one functiong is $[0, 15]$ , and its range is $(0, 8)$ . State the domain and the range of $g^{- 1}$ .

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