A man agrees to pay Rs.4500 per month for 30 moths to pay off a car loan. If the interest of 18% per annum is charged monthly, the present value of car is:

i = .18/12 = .015

n = 30

PV = 4500( 1 - 1.015^-30)/.015
= ....

Why did the car go to the comedy club? Because it had a great sense of mileage! Anyway, let's calculate the present value of the car loan.

To calculate the present value of the car loan, we need to consider the monthly payment, the number of months, and the interest rate. Since the interest rate is 18% per annum, that means it's 1.5% per month (18% divided by 12 months).

Using a financial calculator or formula, we can calculate the present value of the car loan. Let's assume the monthly payment is denoted as P, the number of months is denoted as N, and the interest rate per month is denoted as R.

P = Rs.4500 (monthly payment)
N = 30 months
R = 1.5% (interest rate per month)

Using the formula, the present value of the car loan can be calculated as follows:

Present Value = P * (1 - (1 + R)^-N) / R

Plugging in the values, we get:

Present Value = Rs.4500 * (1 - (1 + 0.015)^-30) / 0.015

Calculating this gives us the present value of the car loan. So, let's calculate it and see what we get!

To calculate the present value of the car, we need to find the loan amount that will be paid off over 30 months with monthly payments of Rs.4500, given an interest rate of 18% per annum charged monthly.

First, we can calculate the monthly interest rate by dividing the annual interest rate by 12:

Monthly interest rate = Annual interest rate / 12 = 18% / 12 = 1.5% or 0.015

Next, we can use the formula for the present value of an ordinary annuity to calculate the loan amount. The formula is:

PV = PMT × [(1 - (1 + r)^(-n)) / r]

Where:
PV = Present Value (loan amount)
PMT = Monthly payment
r = Monthly interest rate
n = Number of periods (months)

Plugging in the given values:
PMT = Rs.4500
r = 0.015
n = 30

PV = Rs.4500 × [(1 - (1 + 0.015)^(-30)) / 0.015]

Now, let's calculate the present value of the car:

PV = Rs.4500 × [(1 - (1.015)^(-30)) / 0.015]
PV = Rs.4500 × [(1 - 0.408778166) / 0.015]
PV = Rs.4500 × (0.591221834 / 0.015)
PV = Rs.4500 × 39.414788934
PV = Rs.177,366.55

Therefore, the present value of the car is approximately Rs.177,366.55.

To calculate the present value of a car loan, we need to find the principal amount or the original value of the car.

The given information includes the monthly payment of Rs. 4500 for 30 months and an interest rate of 18% per annum charged monthly. We'll use the formula for the present value of an annuity to solve for the principal amount.

The formula for the present value of an annuity is:

PV = P * (1 - (1 + r)^(-n)) / r

Where:
PV = Present Value
P = Payment per period
r = Interest rate per period
n = Number of periods

In this case, we have:
Payment per period (P) = Rs. 4500
Interest rate per period (r) = 18% per annum / 12 months = 1.5% per month
Number of periods (n) = 30 months

Now, let's substitute these values into the formula and calculate the present value (PV):

PV = 4500 * (1 - (1 + 0.015)^(-30)) / 0.015

Using a calculator, we can simplify the equation:

PV = 4500 * (1 - 0.982503) / 0.015
PV = 4500 * 0.017497 / 0.015

PV ≈ 5114.98

Therefore, the present value or the original value of the car is approximately Rs. 5114.98.