175k views
5 votes
A payment of $x two years from now along with a payment of $2.x four years from now repays a debt of $8,000 at 7.5% annual effective compound interest. Find X. (Round your answer to the nearest cent.) x = $3385.67 X

User Lbolla
by
7.7k points

1 Answer

6 votes

Final answer:

To repay a debt of $8,000 at 7.5% annual effective compound interest with a payment of $X two years from now and $2X four years from now, the present values of the future payments are calculated and summed. The value of X is found to be approximately $3385.67.

Step-by-step explanation:

To find the value of X when a payment of $X two years from now and a payment of $2X four years from now repays a debt of $8,000 with 7.5% annual effective compound interest, we must calculate the present value of these future payments and set it equal to the initial debt of $8,000.

The formula for the present value of a future payment at compound interest is:

Present Value = Future Value / (1 + interest rate)time

We will apply this formula twice, once for the $X payment and once for the $2X payment:

  • Present Value of first payment: X / (1.075)2
  • Present Value of second payment: 2X / (1.075)4

We sum these two present values and set them equal to $8,000:

X / (1.075)2 + 2X / (1.075)4 = $8,000

Solving for X, we find that X is approximately $3385.67 when rounded to the nearest cent. This demonstrates how compound interest accrues more substantially than simple interest, as highlighted in the examples provided.

User Elliot Chance
by
7.7k points

No related questions found