SOLUTION: A person pays interest on a loan semi-annually at a nominal rate of 16%. What is the effective rate of interest?

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Question 1169921: A person pays interest on a loan semi-annually at a nominal rate of 16%. What is the effective rate of interest?
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
the nominal interest rate percent is 16%.

the interest rate is compounded semi-annually.

divide 16% by 2 to get 8%.

that's your interest rate percent per semi-annual period.

divide that by 100 to get .08.

that's your interest rate per semi-annual period.

add that to 1 to get 1.08.

that's your growth factor per semi-annual time period.

raise that to the second power to get 1.08 ^ 2 = 1.1664.

that's your effective growth factor per year.

subtract 1 from that to get .1664.

that's your effective interest rate per year.

multiply that by 100 to get 16.64%.

that's your effective interest rate percent per year.

your nominal rate percent per year is 16%.

your effective rate percent per year is 16.64%.

let me know if you have any questions regarding this.

theo

Answer by MathTherapy(10549) (Show Source):
You can put this solution on YOUR website!

A person pays interest on a loan semi-annually at a nominal rate of 16%. What is the effective rate of interest?

Effective interest rate formula: , where:
= Annual Interest rate (16%, or .16, in this case)
= Number of ANNUAL compounding periods (semi-annually, or 2, in this case)
= Time, in years (1, in this case)
becomes: