Respuesta :
Solution :
It is given : loan amount = $12,000
Time to repay = 12 months
Finance charge = $ 632
AT the interest rate, outflow = inflow
The present value of the loan amounts = loan amount
[tex]$1000+632+[1000 \times (PVAF (r ,11))]=12000$[/tex]
[tex]$1000 \times PVAF(r,11)=12000-1632$[/tex]
[tex]$PVAF(r,11)=\frac{10368}{1000}$[/tex]
[tex]$PVAF(r,11)=10.368$[/tex]
Now using the annuity table we get
PVAF(1%, 11)=10.9676
This is equal to 10.368 (approximately)
∴ [tex]$r=1$[/tex] % per month of compounded monthly
So the annual interest rate is :
[tex]$=[(1+0.01)^{12}]-1$[/tex]
[tex]$r=[(1.01)^{12}]-1$[/tex]
[tex]$r = 12.68$[/tex] %
= 12.70 %
Hence the correct option is (a).
The loan's effective yearly interest rate is 12.7 percent. As a result, option (a) is the proper response.
How do you compute the Annual Interest rate?
[tex]\text{It is given : loan amount} = $12,000\\\text{Time to repay} = 12 months\text{Finance charge} = $ 632\\\text{At the interest rate, outflow = inflow}\\\text{The present value of the loan amounts = loan amount}[/tex]
[tex]1000 + 632 + [ (P.V (r.11))] = 12,000\\\\1000 \text { x } P.V (r,11) = 12,000 - 1,632\\\\P.V (r.11) = \frac{10,368}{1000}\\\\P.V (r,11) = 10.368[/tex]
[tex]\text{Now using the annuity table we get} \\P.V (0.01, 11) =10.9676\\\text{This is equal to 10.368 (approximately)}[/tex]
[tex]r = 0.01 \text{ per month}\\\text{ Annual Interest rate}:\\r= [(1+0.01}^{12}] - 1\\r= [(1.01}^{12}] - 1\\r= 12.68\\[/tex]
Therefore, the closest option among the following choices is an option (a), i.e., 12.7%
For more information about the annual interest rate, refer below
https://brainly.com/question/16544946
