An initial deposit of $45,000 grows at an annual rate of 10% for 20 years. Compare the final balances resulting from continuous
1 answer:
Answer:
Annual: $302 737.50
Continuous: $332 507.52
Step-by-step explanation:
A. Compounded annually
The formula for <em>compound interest</em> is
A = P(1 + r)ⁿ
Data:
P = $45 000
r = 10 %
t = 20 yr
Calculations:
n = 20
A = 45 000(1+ 0.10)²⁰
= 45 000 × 1.10²⁰
= 45 000 × 6.727 499 95
= $302 737.50
B. Compounded continuously
The formula for <em>continuously compounded inerest</em> is
= 45 000 × 7.389 056 61
= $332 507.52
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the maximum height is the y-value of the vertex.
h(x) = -2x² + 20x + 48
<em> a=-2, b=20, c=48</em>
h(5) = -2(5)² + 20(5) + 48
= -50 + 100 + 48
= 50 + 48
= 98
Answer: 98 meters
Answer:
Josie should purchase floral daisy wallpaper.
Step-by-step explanation:
Area = Length × Width
The area of the Josie's accent wall = 9 × 10 = 90 feet²
The cost of Floral Daisy per square feet
=
=
= 0.98534 ≈ $0.99/ft²
The cost of total wallpaper for the wall = 90 × 0.99 = $89.10
The cost of Flower Power per square feet =
=
= 1.0096 ≈ $1.01/ft²
The cost of total wallpaper for the wall = 90 × 1.01 = $90.90
total savings = 90.90 - 89.10 = $1.80
∵ The floral daisy wallpaper comes in size = 1.45 ft × 9.8 ft
∴ Josie needs the number of rolls of floral daisy wallpaper to cover her wall = 7
The cost of 7 rolls = 14.67 × 7 = $102.69
To cover her wall with flower power wallpaper, she needs the number of rolls = 2
The cost of 2 rolls = 99 × 2 = $198
We can see the cost of floral daisy wallpaper is less than flower power.
Therefore, Josie should purchase floral daisy wallpaper.