Answer:
The expression to compute the amount in the investment account after 14 years is: <em>FV</em> = [5000 ×(1.10)¹⁴] + [3000 ×(1.10)⁸].
Step-by-step explanation:
The formula to compute the future value is:
![FV=PV[1+\frac{r}{100}]^{n}](https://tex.z-dn.net/?f=FV%3DPV%5B1%2B%5Cfrac%7Br%7D%7B100%7D%5D%5E%7Bn%7D)
PV = Present value
r = interest rate
n = number of periods.
It is provided that $5,000 were deposited now and $3,000 deposited after 6 years at 10% compound interest. The amount of time the money is invested for is 14 years.
The expression to compute the amount in the investment account after 14 years is,
![FV=5000[1+\frac{10}{100}]^{14}+3000[1+\frac{10}{100}]^{14-6}\\FV=5000[1+0.10]^{14}+3000[1+0.10]^{8}](https://tex.z-dn.net/?f=FV%3D5000%5B1%2B%5Cfrac%7B10%7D%7B100%7D%5D%5E%7B14%7D%2B3000%5B1%2B%5Cfrac%7B10%7D%7B100%7D%5D%5E%7B14-6%7D%5C%5CFV%3D5000%5B1%2B0.10%5D%5E%7B14%7D%2B3000%5B1%2B0.10%5D%5E%7B8%7D)
The future value is:
![FV=5000[1+0.10]^{14}+3000[1+0.10]^{8}\\=18987.50+6430.77\\=25418.27](https://tex.z-dn.net/?f=FV%3D5000%5B1%2B0.10%5D%5E%7B14%7D%2B3000%5B1%2B0.10%5D%5E%7B8%7D%5C%5C%3D18987.50%2B6430.77%5C%5C%3D25418.27)
Thus, the expression to compute the amount in the investment account after 14 years is: <em>FV</em> = [5000 ×(1.10)¹⁴] + [3000 ×(1.10)⁸].
Answer:
64
Step-by-step explanation:
4^3=64
4*4=16
16*4=64
20,736 * 729 * 4/216 * 64 * 27 = 60,466,176/373,248 = 162
Ans : 162
Make a system of equations:
0.10x + 0.25y = 3.95
x + y = 23
x + y = 23
Subtract 'y' to both sides:
x = -y + 23
Plug in -y + 23 for 'x' in the first equation:
0.10(-y + 23) + 0.25y = 3.95
Distribute 0.10:
-0.10y + 2.3 + 0.25y = 3.95
Subtract 2.3 to both sides:
-0.10y + 0.25y = 1.65
Combine like terms:
0.15y = 1.65
Divide 0.15 to both sides:
y = 11
Plug this into any of the two equations to find 'x':
x + y = 23
x + 11 = 23
Subtract 11 to both sides:
x = 12
So Sally has 11 dimes and 12 quarters.
Answer:
A: 65mm^3
Step-by-step explanation:
Hopefully this helps!