8.3 Compound Interest

# 8.3 Compound Interest - rate To calculate use the future...

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8.3 Compound INTEREST Compound interest is interest that is calculated on the original principal as well as on any accumulated interest. The period of time between two interest payments is called the compounding period. A = P(1 + r / n ) nt , where A is the future value, P is the present value, r is the rate of interest converted to a decimal, n is the number of compounding period in a year, and t is the number of years. Continuous compounding: A = Pe rt Find the future value and amount of interest on \$25,000 invested at 10% for 7 years compounded: 1. monthly. 2. daily 3. Continuously What principal invested at 12% will yield \$10,000 after 5 years compounded: 4. monthly 5. Quarterly 6. Continuously The effective annual yield, or effective rate, is the simple interest rate that produces the same amount of money in an account at the end of one year as when the account is subjected to the stated compound interest
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Unformatted text preview: rate. To calculate, use the future value formula with P = \$100 and t = 1 ; subtract \$100 from the end answer. Find the effective rate of interest for 9¼% compounded: 7. quarterly 8 semi-annually In the examples 5 and 6, the 9.25% is the nominal rate and the 9.58 or 9.46% is the effective yield. The same result can be gotten with the formula 1 1 n r Y n = +- ÷ and converting the decimal result to a percent. 9. At the time of a child’s birth, his grandparents deposit \$15,000 into a mutual fund with an average yield of 8% a year compounded semi-annually. [a] How much will be in the fund on the child’s 21 st birthday? [b] How much should they have invested for the or [c] What average yield on their \$15,000 would child to receive \$100,000 on his 21 st birthday? have resulted in \$100,000?...
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