SOLUTION: You deposit \$10,000.00 in a account that pays 5% interest compound quarterly. A) Find the future value after 1 year. _____ B) Use the future value formula for simple interest to

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 Question 321641: You deposit \$10,000.00 in a account that pays 5% interest compound quarterly. A) Find the future value after 1 year. _____ B) Use the future value formula for simple interest to determine the effective annual yeild. _________Answer by Theo(3458)   (Show Source): You can put this solution on YOUR website!You deposit 10,000. Interest is 5% compounded quarterly. Future value after 1 year = 10000 * (1.05)^4 = 12155.0625 Effective Interest Rate = (12155.0625/10000 - 1) * 100% = 21.550625% Future Value after 1 year at this effective annual interest rate is 10000 * (1.21550625) = 12155.0625. Nominal Interest Rate = 5% * 4 = 20%. The effective annual interest rate is calculated by raising the compound interest rate to the number of compounding periods per year. If the compound rate is 1% and the number of compounding periods per year is 12 then: The nominal interest rate is 1% * 12 = 12%. The effective annual interest rate is 1.01^12 = 1.12682503 Take that and subtract 1 from it and then multiply it by 100% to get 12.682504%. To use in formulas, you need to convert % to decimal equivalent. 1% is equivalent to .01. Multiplication factor for each year is 1 + this number = 1.01 You raise this factor by the number of compounding periods. For 1 year, at monthly compounding, then fv = 10,000 * 1.01^12 For 2 years, at monthly compounding, then fv = 10,000 * 1.01^24 Effective annual interest rate is equal to 1.01^12 = 1.12682503 For 1 year, at effective annual interest rate, then fv = 10,000 * 1.12682503^1 For 2 years, at effective annual interest rate, then fv = 10,000 * 1.12682503^2 If you do the calculations, you will see that: 10,000 * 1.01^24 = 12697.34649 and: 10,000 * 1.12682503^2 = 12697.34649 They are equivalent.