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(13342)   (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.
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