Nazir saved $900 to buy a plasma tv, he borrowed the rest at an interest rate of 18%/a compounded monthy, 2 years later he paid $ 1420.50 for the principal and the interest, how much did the tv originally cost

Well, it seems Nazir really wanted to watch some plasma television, but ended up paying a lot more than he planned! Let's figure out how much that TV originally cost him.

First, we know he saved $900, so that means the remaining amount he borrowed is the difference between the original cost of the TV and $900.

Let's represent the original cost of the TV as 'x'. Therefore, the loan amount would be (x - $900).

Over the two years, Nazir had to pay back $1420.50, which includes both the principal and the interest. Now, with a compounding monthly interest rate of 18%, we need to calculate the monthly interest rate.

The monthly interest rate would be (18% / 12) = 1.5%.

Using this monthly interest rate, we know that the loan amount would grow over the 2-year period. So, the equation we can set up is:

(x - $900)(1 + 0.015)^24 = $1420.50

Now, let's solve for x:

(x - $900)(1.015^24) = $1420.50

Simplifying:

(x - $900)(1.41605227) = $1420.50

Expanding:

1.41605227x - $1,274.4470443 = $1420.50

1.41605227x = $2694.947

Dividing by the coefficient of x:

x ≈ $1,901.95

So, it seems the original cost of that plasma TV was approximately $1,901.95. Nazir might have enjoyed it, but I hope he learned a valuable lesson about loans – they can come back to haunt you with interest!

To find out how much the TV originally cost, we need to calculate the principal amount that Nazir borrowed.

Let's denote the principal amount as P.

After 2 years, the amount Nazir paid, which includes both the principal and the interest, is $1420.50.

The interest rate is 18% per year compounded monthly, which means that the interest will be calculated monthly.

Using the compound interest formula:

A = P(1 + r/n)^(nt)

Where:
A = Total amount (principal + interest)
P = Principal amount
r = Annual interest rate (as a decimal)
n = Number of compounding periods per year
t = Number of years

We can plug in the given values:

1420.50 = P(1 + 0.18/12)^(12*2)

Let's simplify the equation:

1420.50 = P(1 + 0.015)^24

Now we can solve for P by dividing both sides of the equation by (1 + 0.015)^24:

P = 1420.50 / (1 + 0.015)^24

Calculating this value gives us:

P ≈ $1273.18

Therefore, the original cost of the TV was approximately $1273.18.

To find out how much the TV originally cost, we need to determine the principal amount that Nazir borrowed.

We know that Nazir paid a total of $1420.50 after two years, and he originally saved $900. Let's subtract his savings from the total payment to find the borrowed amount:

Borrowed amount = Total payment - Savings
= $1420.50 - $900
= $520.50

Now, we can use the formula for compound interest to find the original principal amount. The formula for compound interest is:

A = P(1 + r/n)^(nt)

where:
A = final amount
P = principal amount (initially borrowed)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years

In this case, A is $1420.50, P is the unknown amount we're solving for, r is 18% (0.18 in decimal form), n is 12 (since interest is compounded monthly), and t is 2 (years).

$1420.50 = P(1 + 0.18/12)^(12*2)

To solve for P, let's isolate it on one side of the equation:

P = $1420.50 / (1 + 0.18/12)^(12*2)

Using a calculator, we can calculate the value of P:

P ≈ $481.55

Therefore, the original cost of the TV was approximately $481.55.

Pt = (Po*r*t)/(1-(1+r)^-t).

r = (18%/12) / 100% = 0.015 = Monthly % rate expressed as a decimal.

t = 12 mo/yr * 2yrs = 24 Months.

Pt=(Po*0.015*24)/(1-(1.015)^-24)= 1420.50.
(Po*0.36)/0.30045608 = 1420.50,
1.198178447*Po = 1420.50,
Po = $1185.55 = Amt. of loan.

C = 900 + 1185.55 = $2085.55 = Cost of
TV.