question 1\n1 pts\nif you invest 50,000 at a 6.07% interest rate compounded continuously for 4 years. how…

Question 1

Explanation:

Step1: Recall continuous - compounding formula

The formula for continuous - compounding is $A = Pe^{rt}$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), $t$ is the time in years, and $A$ is the final amount. First, convert the interest rate $r = 6.07%=0.0607$, $P = 50000$, and $t = 4$. $A=50000\times e^{0.0607\times4}$

Step2: Calculate the final amount

$A = 50000\times e^{0.2428}$. Since $e^{0.2428}\approx1.27497$, then $A = 50000\times1.27497 = 63748.5$.

Step3: Calculate the interest earned

The interest earned $I=A - P$. So $I=63748.5−50000 = 13748.5$.

Answer:

$13748.5$

Question 2

Explanation:

Step1: Recall the effective - interest - rate formula

The formula for the effective interest rate $r_{eff}$ when compounded $n$ times a year is $r_{eff}=(1 +\frac{r}{n})^{n}-1$, where $r$ is the annual interest rate (in decimal form) and $n$ is the number of compounding periods per year. For monthly compounding, $n = 12$ and $r=5% = 0.05$. $r_{eff}=(1+\frac{0.05}{12})^{12}-1$

Step2: Calculate the value inside the parentheses

$1+\frac{0.05}{12}=1+\frac{1}{240}=\frac{240 + 1}{240}=\frac{241}{240}\approx1.004167$

Step3: Raise to the 12th power

$(1.004167)^{12}\approx1.051162$

Step4: Calculate the effective interest rate

$r_{eff}=1.051162 - 1=0.051162$ or $5.12%$ (rounded to the nearest $0.01%$)

Answer:

$5.12%$