Kyoko has 10,000 that she wants to invest. Her bank has...

Kyoko has $\$ 10,000$ that she wants to invest. Her bank has several investment accounts to choose from, all compounding daily. Her goal is to have $\$ 15,000$ by the time she finishes graduate school in 6 years. To the nearest hundredth of a percent, what should her minimum annual interest rate be in order to reach her goal? (Hint: solve the compound interest formula for the interest rate.)

Key Concepts

Compound Interest Formula

This formula calculates the future value of an investment based on the initial principal, interest rate, the number of compounding periods, and time. It is expressed as A = P*(1 + r/n)^(n*t), where A is the amount of money accumulated after n*t compounding periods. Understanding this formula is crucial for assessing investment growth over time.

Daily Compounding

Daily compounding refers to the process where interest is calculated and added to the account balance every day. With n representing the number of compounding periods per year (typically 365 for daily compounding), it increases the effective annual interest rate because interest is being calculated and reinvested more frequently.

Exponential Growth

Exponential growth describes the increase of an amount where the growth rate is proportional to the current value. In financial contexts, it illustrates how investments grow with compound interest, leading to faster accumulation as the balance increases, especially when compounded frequently.

Solving Exponential Equations

When an unknown variable, such as the interest rate, appears in the exponent in the compound interest formula, algebraic manipulation using logarithms becomes necessary. This involves taking the logarithm of both sides to isolate and solve for the variable, a key technique in understanding investment calculations.

Transcript

Please give Ace some feedback