Finance problem

[tim0308]

A goods of price $1,000 can be bought by the following modes:
1/ In cash with a discount of 2.3%

2/ By three prmissory notes of the same face value of $338. The first paid in 3 months, the second in 4 months and the last in 5 months.

3/ By 10 monthly payments of $107, the first is paid in 2 months

This shop uses the monthly interest rate of 1.4%
Which mode do you prefer? Calculate the effective rate of each mode.

I am having problem with this so please help me. Thank you in advance guys

 

[Bob Brown MSEE]

click here

 

[stapel]

A goods of price $1,000 can be bought by the following modes:
1/ In cash with a discount of 2.3%

2/ By three prmissory notes of the same face value of $338. The first paid in 3 months, the second in 4 months and the last in 5 months.

3/ By 10 monthly payments of $107, the first is paid in 2 months

This shop uses the monthly interest rate of 1.4%
Which mode do you prefer? Calculate the effective rate of each mode.

What have you tried so far? Where are you stuck?

Please be complete. Thank you!

 

[tim0308]

Sorry for not reading all the rules. After some thinking, I convert all to the present value and compare them.
1/ PV= 1000*2.3%= 977$
2/ Caculate the present value three times ana the result is $959.21
3/ I calculate like number 2/ and the result is $978.33

So the answer is mode 2.

Please check it for me. Thanks

 

[JeffM]

Sorry for not reading all the rules. After some thinking, I convert all to the present value and compare them.
1/ PV= 1000*2.3%= 977$
2/ Caculate the present value three times ana the result is $959.21
3/ I calculate like number 2/ and the result is $978.33

So the answer is mode 2.

Please check it for me. Thanks

Your computations of PV are correct using the store's rate of interest if the notes are due at the end of the indicated month.

I point out, however, that the interest used by the store is irrelevant to what mode is best for you, which depends on YOUR personal rate of time preference. The question asks you to determine the effective rate of interest for each mode and express your preference. You have the option of paying now $977.00. So the effective rate of interest on mode 2 is the interest rate that makes the sum of the present values of the three notes equal to $977.00.

Let me put it a different way. In the second mode, you are going to pay 1,014 over five months instead of 977 now. What interest rate does that imply? Are you willing to pay that much? What formula is needed for that kind of problem?