Question

Susan invests $33,000 for 7 years. What interest rate must the account pay so there is

40,000 in the account at the end of the 7 years? Round to the nearest percent

Answer 1

To find the interest rate Susan needs for her account to reach $40,000 in 7 years, you can use the formula for compound interest:

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

Where:
A = the future amount ($40,000 in this case)
P = the principal amount ($33,000)
r = the annual interest rate (what we want to find)
n = the number of times interest is compounded per year (assuming it's compounded annually, n = 1)
t = the number of years (7 years in this case)

Now, let's plug in the values:

$40,000 = $33,000(1 + r/1)^(1*7)

Simplify the equation:

1 + r = (40,000 / 33,000)^(1/7)

1 + r ≈ 1.2121

Now, subtract 1 from both sides to find r:

r ≈ 1.2121 - 1 ≈ 0.2121

To express the interest rate as a percentage, multiply by 100:

r ≈ 0.2121 * 100 ≈ 21.21%

So, the interest rate Susan needs for her account to reach $40,000 in 7 years is approximately 21.21%, rounded to the nearest percent, it's 21%.