Question

At what rate would you need to invest $10,000 for 12 years compounded monthly for the investment to reach a balance of 15,000 express your answer to the nearest hundredth of a percent

Answer 1

To find the rate required to turn a $10,000 investment into $15,000 over 12 years with monthly compounding, use the compound interest formula A =
`P(1 + r/n)^((nt))`, solve for r, and round to the nearest hundredth of a percent.

Step-by-step explanation:

To determine the rate at which you would need to invest $10,000 for 12 years compounded monthly for the investment to reach a balance of $15,000, we can use the compound interest formula:

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.

For this problem:

• A = $15,000
• P = $10,000
• n = 12 (since interest is compounded monthly)
• t = 12 years

We need to solve for r. Rearranging the formula to solve for r gives us:

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

Substituting the given values and solving for r:

1.5 =
`(1 + r/12)^((12*12))`

We can now solve for r using logarithms. After calculating, we would round the result to the nearest hundredth of a percent to find the required rate.