Question

armando invests $5,300 in two differen accounts. The first account payed 10%, the second account payed 14% in intrest. At the end of the first year he had earned $642 in intrest. How much was in the total interest earned at the end of the first year ?

Answer 1

To determine the initial investment for a future value of $10,000 with 10% annual compound interest over ten years, we use the compound interest formula, which, when solved for the initial principal (P), provides the amount that needs to be invested, approximately $3,855.54.

Step-by-step explanation:

The student's question is about how to determine how much money should be invested at a certain interest rate to achieve a desired future amount. Specifically, they're asking about the amount of money that needs to be invested at 10% compounded interest annually to have $10,000 in ten years.

To solve this, we need to 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, and t is the time the money is invested for in years.

Rearranging the formula to solve for P gives us: P = A / (1 + r/n)^(nt). Plugging in the values from this specific question: A = $10,000, r = 10% or 0.10, n = 1 (since it's compounded annually), and t = 10, we get P = $10,000 / (1 + 0.10/1)^(1\*10) = $10,000 / (1.10)^10. Calculating the value of P gives us the amount required to be invested initially.

Solving the equation, the amount needed to invest is approximately $3,855.54.