question 1 2 pts jessie invested $75,355 in a mutual fund 7 years ago. if it appreciated 7% annually, what…

Explanation:

Step1: Identify compound - interest formula

The compound - interest formula is $A = P(1 + r)^n$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $n$ is the number of years. For Question 1, $P=$75355$, $r = 0.07$, and $n = 7$. $A_1=75355\times(1 + 0.07)^7$

Step2: Calculate the value

$A_1=75355\times(1.07)^7$ $(1.07)^7\approx1.6057814$ $A_1=75355\times1.6057814\approx121972.77$

For Question 2, we first consider the future - value of the initial amount and then the future - value of the monthly annuity. The future - value of the initial amount $P_0=$100000$ with an annual interest rate $r = 0.075$ for $n = 10$ years is $A_{0}=P_0(1 + r)^n=100000\times(1 + 0.075)^{10}$ $(1.075)^{10}\approx2.061032$ $A_{0}=100000\times2.061032=$206103.2$

The monthly interest rate $i=\frac{0.075}{12}=0.00625$, and the number of periods $m = 10\times12 = 120$, and the monthly payment $C=$600$. The future - value of an ordinary annuity formula is $FVA = C\times\frac{(1 + i)^m-1}{i}$ $FVA=600\times\frac{(1 + 0.00625)^{120}-1}{0.00625}$ $(1 + 0.00625)^{120}\approx2.09756$ $FVA=600\times\frac{2.09756 - 1}{0.00625}=600\times\frac{1.09756}{0.00625}=600\times175.6096=$105365.76$

The total account balance $A_2=A_{0}+FVA=206103.2+105365.76\approx311469$

Answer:

Question 1: $121972.77$ Question 2: $311469$