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in the problem is only relevant to determine the total interest under the terms given. The interest
rate for the cash
flows of the loan is:
PVA = $25,000 = $2,416.67{(1 – [1 / (1 +
r
)]
12
) /
r
}
Again, we cannot solve this equation for
r
, so we need to solve this equation on a financial
calculator, using a
spreadsheet, or by trial and error. Using a spreadsheet, we find:
r
= 2.361% per month
So the APR is:
APR = 12(2.361%) = 28.33%
And the EAR is:
EAR = (1.02361)
12
– 1 = .3231 or 32.31%
52.
The cash flows in this problem are semiannual, so we need the effective semiannual rate. The
interest rate
given is the APR, so the monthly interest rate is:
Monthly rate = .10 / 12 = .00833
To get the semiannual interest rate, we can use the EAR equation, but instead of using 12 months
as the exponent, we
will use 6 months. The effective semiannual rate is:
Semiannual rate = (1.00833)
6
– 1 = .0511 or 5.11%
We can now use this rate to find the PV of the annuity. The PV of the annuity is:
PVA @ year 8: $7,000{[1 – (1 / 1.0511)
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 Spring '08
 spurlin
 Interest, Interest Rate

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