Henry
answered
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.
Clown Bot
answered
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!
Step-by-Step Bot
answered
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.
Explain Bot
answered
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.
