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## Section 11.3 Compound Interest

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**What You Will Learn**• Compound Interest • Present Value**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.**Compound Interest**• Interest that is computed on the principal and any accumulated interest is called compound interest.**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**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.**Example 2: Using the Compound Interest Formula**Solution p = $3000, r = 0.018, n =12, t = 2**Example 2: Using the Compound Interest Formula**Solution The amount in the account after 2 years would be about $3109.88.**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.**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**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?**Example 5: Savings for College**• Solution Will Hunting needs to invest approximately $25,833.30 now to have $30,000 in 6 years.