What is simple interest and how is it calculated?

Simple interest is calculated using the formula I = P * r * t, where I is the interest, P is the principal amount (the initial amount of money), r is the annual interest rate (in decimal), and t is the time in years.

If you invest $1,000 at a simple interest rate of 5% per year for 3 years, how much interest will you earn?

Using the formula

 I = P * r * t

I = 1000 * 0.05 * 3

 = $150

Therefore, you will earn $150 in interest.

What is compound interest and how does it differ from simple interest?

Calculate the total amount in an account after 2 years if $2,000 is invested at an annual interest rate of 4% compounded annually.

Using the compound interest formula

 A = P(1 + r/n)^(nt)

A = 2000(1 + 0.04/1)^(1*2)

= 2000(1.04)²

= 2000 * 1.0816 

= $2163.20.

 So the total amount will be $2163.20.

If a loan of $5,000 has an annual interest rate of 6% compounded quarterly, what is the total amount owed after 3 years?

Using the compound interest formula

 A = P(1 + r/n)^(nt)

A = 5000(1 + 0.06/4)^(4*3) 

= 5000(1 + 0.015)⁽¹²⁾ 

= 5000(1.015)⁽¹²⁾

 Calculating that gives A ≈ 5000 * 1.1956 ≈ $5978.00. Therefore, the total amount owed after 3 years is approximately $5978.00.

What is the formula for calculating the future value of an investment compounded continuously?

The formula for continuous compounding is A = Pe^(rt), where A is the amount of money accumulated after time t, P is the principal amount, r is the annual interest rate, and e is Euler's number (approximately 2.71828).

If $1,000 is invested at an annual interest rate of 3% compounded continuously, what will the investment be worth after 5 years?

Using the formula

 A = Pe^(rt)

A = 1000 * e^(0.03*5)

≈ 1000 * e^0.15 

≈ 1000 * 1.1618 

≈ $1161.83.

How do you convert an annual interest rate to a monthly interest rate?

To convert an annual interest rate to a monthly rate, divide the annual rate by 12.

 For example, if the annual rate is 6%, the monthly rate is 0.06/12 = 0.005 or 0.5%.