You have two options to repay a loan. You can repay $6000 now and $5940 in one year, or you can repay $12,000 in 6 months. Find the annual effective interest rate at which both options have the same value. Answer is 21% but I need the steps to get there.

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You have two options to repay a loan. You can repay $6000 now and $5940 in one year, or you can repay $12,000 in 6 months. Find the annual effective interest rate at which both options have the same value. Answer is 21% but I need the steps to get there.

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Answer:

Answer: effective interest rate = 21%

Working notes for the above answer is as under

We have been provided in the question that, there are two option

1 You can repay $6000 now and $5940 in one year,

2  you can repay $12,000 in 6 months

Now we take any of the option ,Interest rate will remain same

So we can use the follwing formulla

=6000+5940/(1+i ) =12000/(1+i)1/2

We solve this equation  by trial and error method we will get

effective interest rate = 21%

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