Respuesta :
The value of the credit or present value is [tex]\boxed{\$ 14118.477}.[/tex]
Further explanation:
The compound interest rate formula can be expressed as follows,
[tex]\boxed{{\text{PV}} = A \times \frac{{\left[ {1 - {{\left( {1 + \frac{i}{n}} \right)}^{ - n}}} \right]}}{{\frac{i}{n}}}}[/tex]
Here, [tex]A[/tex] represents the amount, [tex]PV[/tex] represents the present value, irepresent the interest rate and [tex]n[/tex] represents the time.
Given:
The number of months are [tex]48{\text{ months}}.[/tex]
The interest rate is [tex]i = 22.6745\%.[/tex]
The amount overdue is [tex]\$ 450.[/tex]
Explanation:
The value of [tex]n[/tex] is [tex]48.[/tex]
The value of [tex]i[/tex] is [tex]22.6745\%.[/tex]
The present value or the amount credit can be obtained as follows,
[tex]\begin{aligned}{\text{PV}} &= {\text{A}} \times \frac{{\left[ {1 - {{\left( {1 + \frac{i}{{12}}} \right)}^{- 48}}} \right]}}{{\frac{i}{{12}}}}\\&= 450 \times \frac{{\left[ {1 - {{\left({1+\frac{{0.226745}}{{12}}} \right)}^{ - 48}}} \right]}}{{\frac{{0.226745}}{{12}}}}\\&= 450 \times \frac{{0.5928}}{{0.0189}}\\&= \$ 14114.30\\\end{aligned}[/tex]
The value of the credit or present value is [tex]\boxed{\$ 14118.477}.[/tex]
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Loan Schedule
Keywords: Monica, Andrea, loan, 48 consecutive, monthly installments, overdue, $450000, per month, rate charged, band, 22.6745%, NAMV, the value of credit.
