Question

question 10
if 9,400 dollars is invested at an interest rate of 7 percent per year, find the value of the investment at the end of 5 years for the following compounding methods.
(a) annual:
your answer is 13183.99
(b) semiannual:
your answer is 13259.63
(c) monthly:
your answer is 13338.87
(d) daily:
your answer is 13339.23
(e) continuously:
your answer is

Explanation:

Step1: Recall the formula for continuous compounding

The formula for continuous compounding is $A = Pe^{rt}$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal), $t$ is the time in years, and $e$ is the base of the natural logarithm (approximately $2.71828$).

Step2: Identify the values of $P$, $r$, and $t$

Given:

• Principal amount $P = 9400$ dollars
• Annual interest rate $r = 7\% = 0.07$
• Time $t = 5$ years

Step3: Substitute the values into the formula

Substitute $P = 9400$, $r = 0.07$, and $t = 5$ into the formula $A = Pe^{rt}$:
$$A = 9400 \times e^{0.07 \times 5}$$

Step4: Calculate the exponent

First, calculate the exponent: $0.07 \times 5 = 0.35$

Step5: Calculate $e^{0.35}$

Using a calculator, $e^{0.35} \approx 1.419067549$

Step6: Calculate the final amount

Multiply $9400$ by $1.419067549$:
$$A = 9400 \times 1.419067549 \approx 13339.235$$

Answer:

13339.24 (rounded to two decimal places)