Solution :
Given :
Principal amount deposited, P = $ 6000
Rate of interest, r = 5%
Number of years, t = 4 years
When the deposited amount is compounded semiannually, i.e. n = 2
Therefore,
Future value,
![$FV = P\left( 1 +\frac{r}{n}\right)^{nt}$](https://tex.z-dn.net/?f=%24FV%20%3D%20P%5Cleft%28%201%20%2B%5Cfrac%7Br%7D%7Bn%7D%5Cright%29%5E%7Bnt%7D%24)
![$FV = 6000\left( 1 +\frac{0.05}{2}\right)^{2 \times 4}$](https://tex.z-dn.net/?f=%24FV%20%3D%206000%5Cleft%28%201%20%2B%5Cfrac%7B0.05%7D%7B2%7D%5Cright%29%5E%7B2%20%5Ctimes%204%7D%24)
![$FV = 6000 \times (1.025)^8$](https://tex.z-dn.net/?f=%24FV%20%3D%206000%20%5Ctimes%20%281.025%29%5E8%24)
= 6000 x 1.2184
= 7310.4
Therefore, after 4 years there will be $ 7310.4 in the amount when compounded semi annually.
When the deposited amount is compounded quarterly, i.e. n = 4
Therefore,
Future value,
![$FV = P\left( 1 +\frac{r}{n}\right)^{nt}$](https://tex.z-dn.net/?f=%24FV%20%3D%20P%5Cleft%28%201%20%2B%5Cfrac%7Br%7D%7Bn%7D%5Cright%29%5E%7Bnt%7D%24)
![$FV = 6000\left( 1 +\frac{0.05}{4}\right)^{4 \times 4}$](https://tex.z-dn.net/?f=%24FV%20%3D%206000%5Cleft%28%201%20%2B%5Cfrac%7B0.05%7D%7B4%7D%5Cright%29%5E%7B4%20%5Ctimes%204%7D%24)
![$FV = 6000 \times (1.0125)^{16}$](https://tex.z-dn.net/?f=%24FV%20%3D%206000%20%5Ctimes%20%281.0125%29%5E%7B16%7D%24)
= 6000 x 1.219889
= 7319.334
Therefore, after 4 years there will be $ 7319.334 in the amount when compounded quarterly.
When the deposited amount is compounded monthly, i.e. n = 12
Therefore,
Future value,
![$FV = P\left( 1 +\frac{r}{n}\right)^{nt}$](https://tex.z-dn.net/?f=%24FV%20%3D%20P%5Cleft%28%201%20%2B%5Cfrac%7Br%7D%7Bn%7D%5Cright%29%5E%7Bnt%7D%24)
![$FV = 6000\left( 1 +\frac{0.05}{12}\right)^{12 \times 4}$](https://tex.z-dn.net/?f=%24FV%20%3D%206000%5Cleft%28%201%20%2B%5Cfrac%7B0.05%7D%7B12%7D%5Cright%29%5E%7B12%20%5Ctimes%204%7D%24)
![$FV = 6000 \times (1.0041667)^{48}$](https://tex.z-dn.net/?f=%24FV%20%3D%206000%20%5Ctimes%20%281.0041667%29%5E%7B48%7D%24)
= 6000 x 1.22089
= 7325.34
Therefore, after 4 years there will be $ 7325.34 in the amount when compounded monthly.
Answer:
y = (4/9)x - 4
Step-by-step explanation:
4x - 9y = 36
4x - 9y - 4x = 36 - 4x
- 9y = -4x + 36
- 9y/(-9) = (-4x + 36)/(- 9)
y = (4/9)x - 4
68% if you take 31 and divide it by 45 you’ll get .68 which you then turn into a percentage
4 + 7x - 3x + 2 = 8x + 6
6 + 4x = 8x + 6
Subtract 6 and 4x from both sides
0 = 4x
0 = x