which investment results in the greatest tota...
which investment results in the greatest total amount? investment a: $4,000 invested for 5 years compounded semiannually at 6%. investment b: $6,000 invested for 4 years compounded quarterly at 2.7%. find the total amount of investment a. $5375.67 (round to the nearest cent as needed.) find the total amount of investment b. $ (round to the nearest cent as needed.)
Answer
# Explanation:
## Step1: Recall compound - interest formula
The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $A$ is the total amount, $P$ is the principal amount, $r$ is the annual interest rate (in decimal), $n$ is the number of times compounded per year, and $t$ is the number of years.
For Investment B, $P = 6000$, $r=0.027$, $n = 4$ (compounded quarterly), and $t = 4$.
## Step2: Substitute values into the formula
$A=6000(1 +\frac{0.027}{4})^{4\times4}$
First, calculate the value inside the parentheses: $\frac{0.027}{4}=0.00675$, and $1+\frac{0.027}{4}=1 + 0.00675=1.00675$.
Then, calculate the exponent: $4\times4 = 16$.
So, $A = 6000\times(1.00675)^{16}$.
## Step3: Calculate $(1.00675)^{16}$
Using a calculator, $(1.00675)^{16}\approx1.11497$.
## Step4: Calculate the total amount $A$
$A=6000\times1.11497 = 6689.82$
# Answer:
$6689.82$