Question

In 1985 George McFly invested $250,000 from his book sale into an account for his son, Marty. The Bank of Hill Valley offered George an interest rate of 9% compounded daily! In what year will Marty first see $1,000,000 in that account?

Answer 1

Marty will first see $1,000,000 in his account approximately 19.7 years after 1985, which is around the year 2005.

Step-by-step explanation:

To find the year in which Marty will first see $1,000,000 in his account, we can use the formula for compound interest:

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

Where:

• A = the final amount
• P = the principal amount (initial investment)
• r = the annual interest rate (in decimal form)
• n = the number of times that interest is compounded per year
• t = the number of years

In this case, George invested $250,000 at an interest rate of 9% compounded daily. We want to find out when the final amount will reach $1,000,000. So, we have:

1,000,000 = 250,000(1 + 0.09/365)^(365t)

To solve for t, we can take the natural logarithm of both sides:

ln(1,000,000/250,000) = ln((1 + 0.09/365)^(365t))

We can simplify the equation using logarithm properties and solve for t:

t = ln(1,000,000/250,000) / (365 * ln(1 + 0.09/365))

Calculating this expression, we find that t ≈ 19.7 years. Therefore, Marty will first see $1,000,000 in his account approximately 19.7 years after 1985, which is around the year 2005.