Exponential Word Problems

Front

What is the formula for compound interest when compounded monthly?

Back

A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, P is the principal amount, r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the number of years.

Front

What does it mean for an investment to be compounded continuously?

Back

Compounding continuously means that the interest is calculated and added to the principal at every possible instant, leading to the formula A = Pe^(rt), where e is Euler's number.

Front

How do you determine if a function represents exponential growth or decay?

Back

If the base of the exponential function is greater than 1, it represents growth. If the base is between 0 and 1, it represents decay.

Front

What is the rule of 70 in relation to exponential growth?

Back

The rule of 70 is a way to estimate the number of years required to double the investment by dividing 70 by the annual growth rate (in percentage).

Front

How do you calculate the future value of an investment after a certain number of years with a fixed interest rate?

Back

Use the formula A = P(1 + r/n)^(nt) for compound interest or A = Pe^(rt) for continuous compounding.

Front

What is the significance of the principal amount in compound interest calculations?

Back

The principal amount is the initial sum of money invested or loaned, which earns interest over time.

Front

How do you find the time required for an investment to double using the continuous compounding formula?

Back

Set A = 2P in the formula A = Pe^(rt) and solve for t: t = ln(2)/r.

Front

What is the impact of a higher interest rate on the future value of an investment?

Back

A higher interest rate increases the future value of an investment, leading to more significant growth over time.

Front

What is the formula to calculate the future value of an investment compounded monthly?

Back

A = P(1 + r/12)^(12t), where r is the annual interest rate and t is the number of years.

Front

How do you calculate the present value needed to reach a future goal with compound interest?

Back

Use the formula P = A / (1 + r/n)^(nt) for compound interest or P = A / e^(rt) for continuous compounding.