Answer:
(a)∴A=$6753.71.
(b)∴A=$1480.24
(c) ∴P=$7424.70
(d)∴P=$49759.62
(e)∴P=$5040.99
(f) ∴P=$2496.11
Step-by-step explanation:
We use the following formula
![A=P(1+\frac rn)^{nt}](https://tex.z-dn.net/?f=A%3DP%281%2B%5Cfrac%20rn%29%5E%7Bnt%7D)
A=amount in dollar
P=principal
r=rate of interest
(a)
P=$2,500, r=5%=0.05,t =20 years , n= 4
![A=\$2500(1+\frac{0.05}{4})^{(20\times 4)](https://tex.z-dn.net/?f=A%3D%5C%242500%281%2B%5Cfrac%7B0.05%7D%7B4%7D%29%5E%7B%2820%5Ctimes%204%29)
=$6753.71
∴A=$6753.71.
(b)
P=$1,000, r=8% =0.08,t =5 years , n= 2
![A=\$1000(1+\frac{0.08}{2})^{(5\times 2)](https://tex.z-dn.net/?f=A%3D%5C%241000%281%2B%5Cfrac%7B0.08%7D%7B2%7D%29%5E%7B%285%5Ctimes%202%29)
=$1480.24
∴A=$1480.24
(c)
A=$10,000, r=6% =0.06,t =5 years , n= 4
![10000=P(1+\frac{0.06}{4})^{(5\times 4)}](https://tex.z-dn.net/?f=10000%3DP%281%2B%5Cfrac%7B0.06%7D%7B4%7D%29%5E%7B%285%5Ctimes%204%29%7D)
![\Rightarrow P=\frac{10000}{(1+0.015)^{20}}](https://tex.z-dn.net/?f=%5CRightarrow%20P%3D%5Cfrac%7B10000%7D%7B%281%2B0.015%29%5E%7B20%7D%7D)
![\Rightarrow P=7424.70](https://tex.z-dn.net/?f=%5CRightarrow%20P%3D7424.70)
∴P=$7424.70
(d)
A=$100,000, r=6% =0.06,t =10 years , n= 12
![100000=P(1+\frac{0.07}{12})^{(10\times 12)}](https://tex.z-dn.net/?f=100000%3DP%281%2B%5Cfrac%7B0.07%7D%7B12%7D%29%5E%7B%2810%5Ctimes%2012%29%7D)
![\Rightarrow P=\frac{100000}{(1+\frac{0.07}{12})^{120}}](https://tex.z-dn.net/?f=%5CRightarrow%20P%3D%5Cfrac%7B100000%7D%7B%281%2B%5Cfrac%7B0.07%7D%7B12%7D%29%5E%7B120%7D%7D)
![\Rightarrow P=49759.62](https://tex.z-dn.net/?f=%5CRightarrow%20P%3D49759.62)
∴P=$49759.62
(e)
A=$100,000, r=10% =0.10,t =30 years , n= 12
![100000=P(1+\frac{0.10}{12})^{(30\times 12)}](https://tex.z-dn.net/?f=100000%3DP%281%2B%5Cfrac%7B0.10%7D%7B12%7D%29%5E%7B%2830%5Ctimes%2012%29%7D)
![\Rightarrow P=\frac{100000}{(1+\frac{0.10}{12})^{360}}](https://tex.z-dn.net/?f=%5CRightarrow%20P%3D%5Cfrac%7B100000%7D%7B%281%2B%5Cfrac%7B0.10%7D%7B12%7D%29%5E%7B360%7D%7D)
![\Rightarrow P=5040.99](https://tex.z-dn.net/?f=%5CRightarrow%20P%3D5040.99)
∴P=$5040.99
(f)
A=$100,000, r=7% =0.07,t =20 years , n= 4
![100000=P(1+\frac{0.07}{4})^{(20\times 4)}](https://tex.z-dn.net/?f=100000%3DP%281%2B%5Cfrac%7B0.07%7D%7B4%7D%29%5E%7B%2820%5Ctimes%204%29%7D)
![\Rightarrow P=\frac{100000}{(1+\frac{0.07}{4})^{80}}](https://tex.z-dn.net/?f=%5CRightarrow%20P%3D%5Cfrac%7B100000%7D%7B%281%2B%5Cfrac%7B0.07%7D%7B4%7D%29%5E%7B80%7D%7D)
![\Rightarrow P=2496.11](https://tex.z-dn.net/?f=%5CRightarrow%20P%3D2496.11)
∴P=$2496.11