Question

Nazir saved $900 to buy a plasma TV. He borrowed the rest at an interest rate of 18%/a compounded monthly. Two years later, he paid $1429.50 for the principal and the interest. How much did the TV originally cost?

Answer 1

To find out the original cost of a TV that Nazir bought, compound interest calculations are performed on the total amount he paid after two years, including the amount he saved and the amount he borrowed. By rearranging the compound interest formula, we can determine the principal borrowed and add it to his savings to get the original price.

Step-by-step explanation:

The student is asking a question on how to determine the original cost of a television Nazir bought using a combination of savings and a loan with compound interest. We know that Nazir saved $900 and later paid $1429.50, which includes both the principal and the compounded interest after two years. To find out how much he borrowed, we will use the formula for compound interest:

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

Where:

• A is the amount of money accumulated after n years, including interest.
• P is the principal amount (the initial amount of money).
• r is the annual interest rate (decimal).
• n is the number of times that interest is compounded per year.
• t is the time the money is invested for, in years.

We rearrange the formula to solve for P:

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

Given that A = $1429.50, r = 18% or 0.18, n = 12 (since the interest is compounded monthly), and t = 2, we can calculate the principal amount (P) that Nazir borrowed. Then we add the $900 he saved to get the original cost of the TV.