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# Effective Annual Rate

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An investment instrument pays \$1.35 million at the end of each of the next ten years. An investor has an alternative investment with the same amount of risk that will pay interest at 8.5 percent, compounded quartely.

What effective rate should you receive in this investment?
How much should you pay for the mortgage instrument?

After the EAR is established, how is the problem set up for the effective rate. And how will you determine what to pay fot the mortgage instrument?

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An investment instrument pays \$1.35 million at the end of each of the next ten years.  An investor has an alternative investment with the same amount of risk that will pay interest at 8.5 percent, compound quartely.
After the EAR is established, how is the problem set up for the effective rate.  And how will you determine what to pay fot the mortgage instrument?
What effective rate should you receive in this investment?
EAR = Effective annual rate = (1+ nominal rate / Compounding frequency) ^ compounding frequency -1
(^ means raised to the power of)

Nominal rate (APR) = 8.50%
Compounding= Q Quartely
Compounding frequency= 4
Interest rate per period= 2.1250% =9% / 4
EAR (Effective annual rate)= 8.77% =(1+0.02125) ^ 4-1

Answer: Effective annual rate= 8.77%

How much should you pay for the mortgage instrument?

We should pay the present value of annuity

n= 10
r= 8.77%
PVIFA (10 periods, 8.77% rate ) = 6.483143

Annuity= \$1.35 million
Therefore, present value= \$8.75 =1.35x6.483143

PVIFA = present value factor for annuity (either read from tables or calculated using the equation: PVIFA( n, r%)= =[1-1/(1+r%)^n]/r%