Respuesta :
Answer:
D. $31,337.27
Step-by-step explanation:
We have that the initial amount of the loan is $5500.
Miranda took the loan for 4 years. So, the total present value is $5500×4 = $22,000.
The rate of interest on the loan is 7.5% i.e. 0.075 and it was for the duration of 10 years.
Also, it is given that the loan was compounded annually.
We have the formula as,
[tex]P=\frac{\frac{r}{n}\times PV}{1-(1+\frac{r}{n})^{-t\times n}}[/tex]
i.e. [tex]PV=\frac{P\times [1-(1+\frac{r}{n})^{-t\times n}]}{\frac{r}{n}}[/tex]
Substituting the values, we get,
i.e. [tex]PV=\frac{P\times [1-(1+\frac{0.075}{12})^{-10\times 12}]}{\frac{0.075}{12}}[/tex]
i.e. [tex]22000=\frac{P\times [1-(1+0.00625)^{-120}]}{0.00625}[/tex]
i.e. [tex]22000=\frac{P\times [1-(1.00625)^{-120}]}{0.00625}[/tex]
i.e. [tex]22000=\frac{P\times [1-0.4735]}{0.00625}[/tex]
i.e. [tex]22000=\frac{P\times 0.5265}{0.00625}[/tex]
i.e. [tex]P=\frac{22000\times 0.00625}{0.5265}[/tex]
i.e. [tex]P=\frac{137.5}{0.5265}[/tex]
i.e. [tex]P=261.16[/tex]
Thus, the total lifetime cost to pay of the loans compounded annually = 261.16 × 120 = $31,339.2
Hence, the total cost close to the answer is $31,337.27
