Question

You expect to receive a payout from a trust fund in 3 years. The payout will be for $11,800. You plan to invest the money at an annual rate of 6.8 percent until the account is worth $20,200. How many years do you have to wait from today?

Answer 1

By using the compound interest formula, we can find the number of years needed for an investment of $11,800 to grow to $20,200 at a rate of 6.8%. additionally, we must account for the initial 3-year wait for the trust fund payout when calculating the total number of years from today.

Step-by-step explanation:

To determine how many years you have to wait from today until the trust fund payout grows to $20,200 at an annual rate of 6.8%, we can use the formula for compound interest:

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

Where:

• A is the future value of the investment/loan, including interest
• P is the principal investment amount ($11,800)
• r is the annual interest rate (decimal)
• n is the number of times that interest is compounded per year
• t is the number of years the money is invested

Assuming the interest is compounded once a year (n = 1) and converting the interest rate to a decimal (6.8% = 0.068), the formula becomes:

A = $11,800(1 + 0.068)t

To find the number of years required, you substitute A with $20,200 and solve for t. However, you also have to account for the additional 3 years you must wait to receive the initial payout. The calculation of the interest-periods t is separate from these 3 years, so they have to be added together for the total wait time from today.