Question

Payments of $ 670 are being made at the end of each month for 5 years at an interest of 8% compounded monthly. Calculate the Present Value.

Answer 1

Answer:

Present value of the loan is $ 33043.35 ( approx )

Step-by-step explanation:

Since,

The monthly payment formula of a loan,

$P=\frac{PV(\frac{r}{12})}{1-(1+\frac{r}{12})^{-n}}$

Where,

PV = present value of loan,

r = annual interest rate,

n = number of payments.

Here, P = $ 670, r = 8% = 0.08,

Number of months in 5 years, n = 12 × 5 = 60,

By substituting the values in the above formula,

$670 =\frac{PV(\frac{0.08}{12})}{1-(1+\frac{0.08}{12})^{-60}}$

$\implies PV = \frac{670(1-(1+\frac{0.08}{12})^{-60}}{\frac{0.08}{12}}=\ 33043.35$  

Hence, present value of the loan would be $ 33043.35.

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Total payment of a loan

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Answer 2

Given:

Monthly Payment, P = $670

Annual interest rate, r = 8% i.e., r = 0.08

In 5 years, number of months, n = 12 × 5 = 60

To Find:

The present value of loan, PV = ?

Solution:

As we know,

$P=\frac{PV(\frac{r}{12})}{1-(1+\frac{5}{12})^{-n} }$

When we put the appropriate values throughout the formulation above, we get

⇒  $670=\frac{PV(\frac{0.08}{12})}{1-(1+\frac{0.08}{12})^{-60}}$

On applying cross-multiplication, we get

⇒  $PV = \frac{670(1-(1+\frac{0.08}{12})^{-60}))}{\frac{0.08}{12} }$

⇒         $=33043.35$

So that the present value will be "$33043.35".