Comparison of two financial transactions: oose the one that is most convenient based on the REA being the assessment rate of 8%

[Lucio]

Consider the following two Financial Transactions
(a) Investment of 10000 euros today that yields a deferred annual return of 4000 euros per year for 4 years.
(b) Investment of 20000 euros today for 3 years: the principal is repaid in full in 3 years, in the meantime annual interest is paid in arrears at the rate of 10% per year.
Choose the one that is most convenient based on the REA being the assessment rate of 8%

 

[stapel]

Consider the following two Financial Transactions
(a) Investment of 10000 euros today that yields a deferred annual return of 4000 euros per year for 4 years.
(b) Investment of 20000 euros today for 3 years: the principal is repaid in full in 3 years, in the meantime annual interest is paid in arrears at the rate of 10% per year.
Choose the one that is most convenient based on the REA being the assessment rate of 8%

What formula(s) have they given you? What method(s) have you tried? Where are you getting bogged down?

Please be complete. Thank you!

 

[Sajid Eric]

To determine which investment is more convenient based on the REA (Rate of Equivalent Annuity) of 8%, we need to compare the present value of the future cash flows for both options using the given rates and durations.

Let's calculate the equivalent annuities for both options and compare them:

Option (a): Investment: 10000 euros Deferred Annual Return: 4000 euros for 4 years REA: 8%

The equivalent annuity formula is: Equivalent Annuity=Annual Return(1−(1+REA)−Number of Years)/REAEquivalent Annuity=(1−(1+REA)−Number of Years)/REAAnnual Return

Plugging in the values: Equivalent Annuity (Option a)=4000(1−(1+0.08)−4)/0.08≈3176.65 eurosEquivalent Annuity (Option a)=(1−(1+0.08)−4)/0.084000≈3176.65 euros

Option (b): Investment: 20000 euros Annual Interest Rate: 10% Duration: 3 years REA: 8%

For Option (b), we need to calculate the annual interest payments and the principal repayment: Interest Payment (Year 1)=20000×0.10=2000 eurosInterest Payment (Year 1)=20000×0.10=2000 euros Interest Payment (Year 2)=20000×0.10=2000 eurosInterest Payment (Year 2)=20000×0.10=2000 euros Interest Payment (Year 3)=20000×0.10=2000 eurosInterest Payment (Year 3)=20000×0.10=2000 euros Principal Repayment (Year 3)=20000 eurosPrincipal Repayment (Year 3)=20000 euros

Now, we can calculate the equivalent annuity using the same formula as above:

[math]Equivalent Annuity (Option b)= (1−(1+REA) −Number of Years )/REA Interest Payment (Year 1)+Interest Payment (Year 2)+Interest Payment (Year 3)+Principal Repayment (Year 3) Plugging in the values: Equivalent Annuity (Option b) = 2000 + 2000 + 2000 + 20000 ( 1 − ( 1 + 0.08 ) − 3 ) / 0.08 ≈ 6875.03 euros Equivalent Annuity (Option b)= (1−(1+0.08) −3 )/0.08 2000+2000+2000+20000 ≈6875.03 euros[/math]
Comparing the two equivalent annuities, we see that Option (a) has a lower equivalent annuity (3176.65 euros) compared to Option (b) (6875.03 euros). Therefore, based on the given REA of 8%, Option (a) is the more convenient choice.

 

[The Highlander]

To determine which investment is more convenient based on the REA (Rate of Equivalent Annuity) of 8%, we need to compare the present value of the future cash flows for both options using the given rates and durations.

Let's calculate the equivalent annuities for both options and compare them:

Option (a): Investment: 10000 euros Deferred Annual Return: 4000 euros for 4 years REA: 8%

The equivalent annuity formula is: Equivalent Annuity=Annual Return(1−(1+REA)−Number of Years)/REAEquivalent Annuity=(1−(1+REA)−Number of Years)/REAAnnual Return

Plugging in the values: Equivalent Annuity (Option a)=4000(1−(1+0.08)−4)/0.08≈3176.65 eurosEquivalent Annuity (Option a)=(1−(1+0.08)−4)/0.084000≈3176.65 euros

Option (b): Investment: 20000 euros Annual Interest Rate: 10% Duration: 3 years REA: 8%

For Option (b), we need to calculate the annual interest payments and the principal repayment: Interest Payment (Year 1)=20000×0.10=2000 eurosInterest Payment (Year 1)=20000×0.10=2000 euros Interest Payment (Year 2)=20000×0.10=2000 eurosInterest Payment (Year 2)=20000×0.10=2000 euros Interest Payment (Year 3)=20000×0.10=2000 eurosInterest Payment (Year 3)=20000×0.10=2000 euros Principal Repayment (Year 3)=20000 eurosPrincipal Repayment (Year 3)=20000 euros

Now, we can calculate the equivalent annuity using the same formula as above:

[math]Equivalent Annuity (Option b)= (1−(1+REA) −Number of Years )/REA Interest Payment (Year 1)+Interest Payment (Year 2)+Interest Payment (Year 3)+Principal Repayment (Year 3) Plugging in the values: Equivalent Annuity (Option b) = 2000 + 2000 + 2000 + 20000 ( 1 − ( 1 + 0.08 ) − 3 ) / 0.08 ≈ 6875.03 euros Equivalent Annuity (Option b)= (1−(1+0.08) −3 )/0.08 2000+2000+2000+20000 ≈6875.03 euros[/math]
Comparing the two equivalent annuities, we see that Option (a) has a lower equivalent annuity (3176.65 euros) compared to Option (b) (6875.03 euros). Therefore, based on the given REA of 8%, Option (a) is the more convenient choice.

The aim of the forum is to help members with their problems (the clue is in the forum's name), not to provide them with a complete solution! ?

Doing so doesn't help them in any way, it simply does their work for them and they benefit in no way from that. ?‍

 

[Dr.Peterson]

The aim of the forum is to help members with their problems (the clue is in the forum's name), not to provide them with a complete solution! ?

Doing so doesn't help them in any way, it simply does their work for them and they benefit in no way from that. ?‍

On the other hand, it's been a month and the OP never responded to two requests for information. We do tend to allow full answers in such a situation. (I haven't checked whether the answer is correct, though.)

 

[The Highlander]

On the other hand, it's been a month and the OP never responded to two requests for information. We do tend to allow full answers in such a situation. (I haven't checked whether the answer is correct, though.)

Ooops! ?
Sorry, my bad. ?

I'm afraid I didn't check the dates (properly). I just noticed that both the OP, @Lucio, and @Sajid Eric (who had only just joined today it appeared) were "New members" and assumed that the question posted was a fresh one because it was at the top of the "Latest posts" list but, of course, it was @Sajid Eric's (perfectly legitimate) response that put it there.

Apologies to all (except @Lucio? ?).

 

[Steven G]

Does your nice apology excuse you from going into the corner to think about what you have done?
I personally think that you thought about it enough and should not get any detention.

 

[The Highlander]

Does your nice apology excuse you from going into the corner to think about what you have done?
I personally think that you thought about it enough and should not get any detention.

Thank you for your sympathetic comment, Steven. ?

I can understand your empathy since we both have stools with our names on them over there. ?

However, it's no bad thing to spend some time in the corner occasionally as it not only provides a good opportunity to reflect on our (frequent?) solecisms but that's also where I get the time to create the pretty (useful?) pictures I post from time to time. ?

See you (back) there soon? ?