Respuesta :
Answer:
Part 1) Option A
a) [tex]A=\$53,750[/tex]
b) [tex]A=\$57,500[/tex]
c) [tex]A=\$65,000[/tex]
Part 2) Option B
a) [tex]A=\$53,864[/tex]
b) [tex]A=\$58,027[/tex]
c) [tex]A=\$67,343[/tex]
Step-by-step explanation:
Part 1) Option A
Simple Interest
we know that
The simple interest formula is equal to
[tex]A=P(1+rt)[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
in this problem we have
case a) 5 years
[tex]t=5\ years\\ P=\$50,000\\r=1.5\%=1.5/100=0.015[/tex]
substitute in the formula above
[tex]A=50,000(1+0.015*5)[/tex]
[tex]A=50,000(1.075)[/tex]
[tex]A=\$53,750[/tex]
case b) 10 years
[tex]t=10\ years\\ P=\$50,000\\r=1.5\%=1.5/100=0.015[/tex]
substitute in the formula above
[tex]A=50,000(1+0.015*10)[/tex]
[tex]A=50,000(1.15)[/tex]
[tex]A=\$57,500[/tex]
case c) 20 years
[tex]t=20\ years\\ P=\$50,000\\r=1.5\%=1.5/100=0.015[/tex]
substitute in the formula above
[tex]A=50,000(1+0.015*20)[/tex]
[tex]A=50,000(1.30)[/tex]
[tex]A=\$65,000[/tex]
Part 2) Option B
interest compounded annually
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
case a) 5 years
[tex]t=5\ years\\ P=\$50,000\\r=1.5\%=1.5/100=0.015\\n=1[/tex]
substitute in the formula above
[tex]A=50,000(1+\frac{0.015}{1})^{1*5}[/tex]
[tex]A=50,000(1.015)^{5}[/tex]
[tex]A=\$53,864[/tex]
case b) 10 years
[tex]t=10\ years\\ P=\$50,000\\r=1.5\%=1.5/100=0.015\\n=1[/tex]
substitute in the formula above
[tex]A=50,000(1+\frac{0.015}{1})^{1*10}[/tex]
[tex]A=50,000(1.015)^{10}[/tex]
[tex]A=\$58,027[/tex]
case c) 20 years
[tex]t=20\ years\\ P=\$50,000\\r=1.5\%=1.5/100=0.015\\n=1[/tex]
substitute in the formula above
[tex]A=50,000(1+\frac{0.015}{1})^{1*20}[/tex]
[tex]A=50,000(1.015)^{20}[/tex]
[tex]A=\$67,343[/tex]
Answer:
Option A-
5 years: $53,750
10 years:$57,500
20 years:$65,000
Option B-
5 years:$53,599
10 years:$57,458
20 years:$66,028
Step-by-step explanation:
