Question 1182272: You apply for a $1100 loan, which you plan to repay in 5 years. You are told by the loan officer that the amount payable when the loan is due is $2700. What rate of interest, compounded bi-weekly, are you being charged? Round answers to 2 decimal places.
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! f = p * (1 + r) ^ n
f is the future value
p is the present value
r is the interest rate per time period
n is the number of time periods
in your problem:
p = 1100
n = 5 years * 26 = 130 bi-weekly periods.
f = 2700
you are solving for r.
formula becomes:
2700 = 1100 * (1 + r) ^ 130
divide both sides of this equation by 1100 to get:
2700/1100 = (1 + r) ^ 130
take the 130th root of both sides of this equation to get:
(2700/1100)^(1/130) = 1 + r
solve for 1 + r to get:
1 + r = 1.006931153
subtract 1 from both sides of that equation to get:
r = .006931153
that's the rate for every bi-week.
multiply that by 26 to get:
r = .1802099792 per year.
that's the nominal interest rate per year.
confirm by doing the following.
divide .1802099792 by 26 to get:
r = .006931153
add 1 to that to get:
1 + r = 1.0069311563
use that in your equation to get:
f = 1100 * 1.0069311563 ^ 130\
solve for f to get:
f = 2700.
this confirms the bi-weekly interest rate is correct.
the bi-weekly interest rate is .0069311563.
multiply that by 100 to get .69311563% every two weeks.
if you look up the definition of bi-weekly, you will find that there is ambiguity in the definition.
it could mean every two weeks, or it could mean twice a week.
i'm assuming it means every two weeks.
if that turns out to be incorrect, then let me know and i'll revise the figures for twice a week.
what would be done in that case is:
number of time periods = 2 * 52 * 5 = 520
you would then use that number rather than 130 in the formula.
the nominal interest rate per year would then be your answer * 520 rather than your previous answer * 130.
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website! You apply for a $1100 loan, which you plan to repay in 5 years. You are told by the loan officer that the amount payable when the loan is due is $2700. What rate of interest, compounded bi-weekly, are you being charged? Round answers to 2 decimal places.
Use the formula for the interest rate of a SINGLE amount.
This is:  , where:  = Accumulated amount, or future value ($2,700, in this case)
 = Present Value, or Principal invested, or INITIAL amount deposited ($1,100, in this case)
 = Annual Interest rate (UNKNOWN, in this case)
 = Number of ANNUAL compounding periods (Bi-weekly, or every 2 weeks, or 26, in this case)
 = Time, in years (5, in this case)
then becomes: 
Interest rate, or 
If bi-weekly means every 2 weeks, then change m, or 26 above, to 2(52), or 104, and re-calculate.
Capeesh/Capiche/Capisce?
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