Question

you just won $17,500 and deposited your winnings into an account that pays 6.7 percent interest, compounded annually. how long will you have to wait until your winnings are worth $50,000?

Answer 1

To determine how long it will take for your winnings to reach $50,000, you can use the compound interest formula. Plugging in the values, we find that it will take approximately 14.105 years for your winnings to be worth $50,000.

To determine how long it will take for your winnings to reach $50,000, you can use the compound interest formula:

Amount = Principal (1 + Rate/100)^Time

Where:

Amount is the final value you want to achieve ($50,000)

Principal is the initial deposit ($17,500)

Rate is the interest rate (6.7%)

Time is the number of years

Plugging in the values, we get:

$50,000 = $17,500 (1 + 6.7/100)^Time

Simplifying the equation:

2.8571 = (1.067)^Time

Taking the natural logarithm of both sides:

ln(2.8571) = ln(1.067)^Time

Applying the logarithmic properties:

ln(2.8571) = Time * ln(1.067)

Dividing both sides by ln(1.067), we get:

Time = ln(2.8571) / ln(1.067)

Using a calculator:

Time ≈ 14.105

Therefore, you will have to wait approximately 14.105 years for your winnings to be worth $50,000.