Question

Amelia is going to invest $90,000 and leave it in an account for 12 years. Assuming the interest is compounded monthly, what interest rate, to the nearest hundredth of a percent, would be required in order for Amelia to end up with $ 44, 000 ?

Answer 1

To find the interest rate required for Amelia to end up with $44,000 in 12 years with monthly compounding, the formula for compound interest is used. The interest rate is approximately 2.06%.

Step-by-step explanation:

To find the interest rate required for Amelia to end up with $44,000 in 12 years with monthly compounding, we can use the formula for compound interest:

A = P(1 + r/n)nt

Where:

• A = The future value of the investment ($44,000)
• P = The initial investment ($90,000)
• r = The interest rate
• n = The number of times the interest is compounded per year (12)
• t = The number of years (12)

Substituting these values into the formula, we get:

$44,000 = $90,000(1 + r/12)12*12

Simplifying the equation, we can solve for r by rearranging:

1 + r/12 = (44000/90000)1/(12*12)

r/12 = (44000/90000)1/(12*12) - 1

r = ( (44000/90000)1/(12*12) - 1 ) * 12

Using a calculator, we find that the interest rate is approximately 2.06%.