Answer:
option-C
option-D
Step-by-step explanation:
we are given
He estimates that he can afford monthly payments of $265 for 10 years in order to support his loan
so, firstly we will find total amount
![A=265\times 12\times 10](https://tex.z-dn.net/?f=A%3D265%5Ctimes%2012%5Ctimes%2010)
![A=31800](https://tex.z-dn.net/?f=A%3D31800)
now, we can verify each options
option-A:
r=6.6% =0.066
Amount is same
![A=31800](https://tex.z-dn.net/?f=A%3D31800)
now, we can use APR formula
![A=P(1+\frac{r}{n})^{nt}](https://tex.z-dn.net/?f=A%3DP%281%2B%5Cfrac%7Br%7D%7Bn%7D%29%5E%7Bnt%7D)
It is compounded monthly
so, n=12
we can plug it and then we can solve for P
![31800=P(1+\frac{0.066}{12})^{12\times 10}](https://tex.z-dn.net/?f=31800%3DP%281%2B%5Cfrac%7B0.066%7D%7B12%7D%29%5E%7B12%5Ctimes%2010%7D)
![P=16465.6215](https://tex.z-dn.net/?f=P%3D16465.6215)
we can see that it is less than 24418.05
So, this is FALSE
option-B:
r=6.2% =0.062
Amount is same
![A=31800](https://tex.z-dn.net/?f=A%3D31800)
now, we can use APR formula
![A=P(1+\frac{r}{n})^{nt}](https://tex.z-dn.net/?f=A%3DP%281%2B%5Cfrac%7Br%7D%7Bn%7D%29%5E%7Bnt%7D)
It is compounded monthly
so, n=12
we can plug it and then we can solve for P
![31800=P(1+\frac{0.062}{12})^{12\times 10}](https://tex.z-dn.net/?f=31800%3DP%281%2B%5Cfrac%7B0.062%7D%7B12%7D%29%5E%7B12%5Ctimes%2010%7D)
![P=17133.96](https://tex.z-dn.net/?f=P%3D17133.96)
we can see that it is less than 24418.05
So, this is FALSE
option-C:
r=5.2% =0.052
Amount is same
![A=31800](https://tex.z-dn.net/?f=A%3D31800)
now, we can use APR formula
![A=P(1+\frac{r}{n})^{nt}](https://tex.z-dn.net/?f=A%3DP%281%2B%5Cfrac%7Br%7D%7Bn%7D%29%5E%7Bnt%7D)
It is compounded monthly
so, n=12
we can plug it and then we can solve for P
![31800=P(1+\frac{0.052}{12})^{12\times 10}](https://tex.z-dn.net/?f=31800%3DP%281%2B%5Cfrac%7B0.052%7D%7B12%7D%29%5E%7B12%5Ctimes%2010%7D)
![P=18927.00451](https://tex.z-dn.net/?f=P%3D18927.00451)
we can see that it is less than 24418.05
So, this is TRUE
option-D:
r=5.8% =0.058
Amount is same
![A=31800](https://tex.z-dn.net/?f=A%3D31800)
now, we can use APR formula
![A=P(1+\frac{r}{n})^{nt}](https://tex.z-dn.net/?f=A%3DP%281%2B%5Cfrac%7Br%7D%7Bn%7D%29%5E%7Bnt%7D)
It is compounded monthly
so, n=12
we can plug it and then we can solve for P
![31800=P(1+\frac{0.058}{12})^{12\times 10}](https://tex.z-dn.net/?f=31800%3DP%281%2B%5Cfrac%7B0.058%7D%7B12%7D%29%5E%7B12%5Ctimes%2010%7D)
![P=17829.66](https://tex.z-dn.net/?f=P%3D17829.66)
we can see that it is less than 24418.05
So, this is TRUE