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xeze [42]
2 years ago
14

You have two options to repay a loan. You can repay $6,000 now and $5,940 in one year; or you can repay $12,000 in 6 months. Fin

d the annual effective interest rate(s) i at which both options have the same present value.
Business
1 answer:
Brums [2.3K]2 years ago
7 0

Answer:

We will consider positive interest rate which is i=0.21 or i=21%

Explanation:

The formula for Future value is:

FV=PV(1+i)^n

The present value will become:

PV=FV(1+i)^{-n}

where:

n is the number of years

Since the condition is same present value,so the given data form the equation:

6000+5940(1+i)^{-1}=12000(1+i)^{-1/2}

Divide above equation by (1+i)^{-1}

6000(1+i)+5940=12000(1+i)^{1/2}

Let z=(1+i)^{1/2}\\. Above equation will become:

6000z^2+5940=12000z

Rearranging above equation:

5940-12000z+6000z^2=0

Solving the quadratic equation:

z=1.1,    z=0.9

Let z=(1+i)^{1/2}\\ will become:

z=(1+i)^{1/2}\\\\z^2=1+i

i=z^2-1

For z=1.1

i=(1.1)^2-1\\i=0.21

For z=0.9

i=(0.9)^2-1\\i=-0.19

we will consider positive interest rate which is i=0.21 or i=21%

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2 years ago
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Answer:

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Answer:

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2 years ago
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