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Understanding Compound Interest and Present Value Investments

Learn about compound interest, present value investments, and how to calculate future savings with examples. Understand fixed and variable investments, compound interest formula, and annual percentage yield. Plan for future expenses by investing wisely now.

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Understanding Compound Interest and Present Value Investments

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  1. Section 11.3Compound Interest

  2. What You Will Learn • Compound Interest • Present Value

  3. Investments • An investment is the use of money or capital for income or profit. In a fixed investment, the amount invested as principal is guaranteed and the interest is computed at a fixed rate. In avariable investment, neither the principal nor the the interest is guaranteed.

  4. Compound Interest • Interest that is computed on the principal and any accumulated interest is called compound interest.

  5. Compound Interest Formula A is the amount that accumulates in the account p is the principal r is the annual interest rate as a decimal t is the time in years n is the number of compound periods per year

  6. Example 2: Using the Compound Interest Formula Kathy Mowers invested $3000 in a savings account with an interest rate of 1.8% compounded monthly. If Kathy makes no other deposits into this account, determine the amount in the savings account after 2 years.

  7. Example 2: Using the Compound Interest Formula Solution p = $3000, r = 0.018, n =12, t = 2

  8. Example 2: Using the Compound Interest Formula Solution The amount in the account after 2 years would be about $3109.88.

  9. Annual Percent Yield • The effective annualyieldor annual percentage yield (APY) is the simple interest rate that gives the same amount of interest as a compound rate over the same period of time.

  10. Present Value Formula p is the present value, or principal to invest now A is the amount to be accumulated in the account r is the annual interest rate as a decimal n is the number of compound periods per year t is the time in years

  11. Example 5: Savings for College • Will Hunting would like his daughter to attend college in 6 years when she finishes high school. Will would like to invest enough money in a certificate of deposit (CD) now to pay for his daughter’s college expenses. If Will estimates that he will need $30,000 in 6 years, how much should he invest now in a CD that has a rate of 2.5% compounded quarterly?

  12. Example 5: Savings for College • Solution Will Hunting needs to invest approximately $25,833.30 now to have $30,000 in 6 years.

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