Question

using table 11-1, calculate the compound amount and compound interest (in $) for the investment. (round your answers to the nearest cent.) principal: $6,000 time period (years): 4 nominal rate (%): 11 interest compounded: annually compound amount: $\square$ compound interest: $\square$

Explanation:

Step1: Define compound amount formula

The formula for compound amount (compounded annually) is:
$$A = P(1 + r)^t$$
Where $P = 6000$, $r = \frac{11}{100} = 0.11$, $t = 4$

Step2: Calculate the compound amount

Substitute values into the formula:
$$A = 6000(1 + 0.11)^4 = 6000(1.11)^4$$
First compute $(1.11)^4 = 1.11\times1.11\times1.11\times1.11 = 1.51807041$
Then $A = 6000\times1.51807041 = 9108.42246$
Round to nearest cent: $A = 9108.42$

Step3: Calculate compound interest

Compound interest $I = A - P$
$$I = 9108.42 - 6000 = 3108.42$$

Answer:

Compound Amount: $\$9108.42$
Compound Interest: $\$3108.42$