1 point Ramon and Stephen are each considering taking out a $1200 loan so they
can buy dirt bikes to enjoy on the weekend. Ramon's bank is offering him a
4.3% interest rate, while Stephen's is offering him a 2.4% interest
rate. Which of the following statements is TRUE. *
If each loan has a term of 3 years, Ramon's monthly payments will be higher
If they both make $300 payments a month, Ramon will pay off his loan faster
Both men would likely get a better interest rate if they used a credit card, rather than a
personal loan, to make their purchases
If Ramon applies to Stephen's bank, instead, for his loan, he's guaranteed to get the
same 2.4% interest rate that Stephen's been offered

Based on the summary below, the first statement is true. That is, it is true that if each loan has a term of 3 years, Ramon's monthly payments will be higher. This is because Ramon’s monthly payments of $35.59 is higher than Stephen's monthly payments of $34.58.

Step-by-step explanation:

(a) If each loan has a term of 3 years, Ramon's monthly payments will be higher.

The monthly rate can be calculated using the formula for calculating the present value of an ordinary annuity as follows:

PV = P * ((1 - (1 / (1 + r))^n) / r) …………………………………. (1)

Where;

For Ramon:

PV = Present value of loan = $1,200

P = Monthly payments = ?

r = Monthly interest rate = 4.3% / 12 = 0.043 / 12 = 0.00358333333333333

n = number of months = 3 years * 12 months = 36

Substitute the values into equation (1) and solve for P, we have:

$1,200 = P * ((1 - (1 / (1 + 0.00358333333333333))^36) / 0.00358333333333333)

$1,200 = P * 33.7181420201235

P = $1,200 / 33.7181420201235

P = 35.5891495825547

Approximating to 2 decimal places, we have:

P = $35.59

Therefore, Ramon's monthly payments is $35.59.

For Stephen:

PV = Present value of loan = $1,200

P = Monthly payments = ?

r = Monthly interest rate = 2.4% / 12 = 0.024 / 12 = 0.002

n = number of months = 3 years * 12 months = 36

Substitute the values into equation (1) and solve for P, we have:

$1,200 = P * ((1 - (1 / (1 + 0.002))^36) / 0.002)

$1,200 = P * 34.7010963779533

P = $1,200 / 34.7010963779533

P = $34.5810399455389

Approximating to 2 decimal places, we have:

P = $34.58

Therefore, Stephen's monthly payments is $34.58.

(b) If they both make $300 payments a month, Ramon will pay off his loan faster

To determine this we also make use of equation (1) in part (a) as follows:

Where;

For Ramon:

PV = Present value of loan = $1,200

P = Monthly payments = $300

r = Monthly interest rate = 4.3% / 12 = 0.043 / 12 = 0.00358333333333333

n = number of months = ?

Substitute the values into equation (1) and solve for n, we have:

1,200 = 300 * ((1 - (1 / (1 + 0.00358333333333333))^n) / 0.00358333333333333)

1,200 / 300 = (1 - (1 / (1 + 0.00358333333333333))^n) / 0.00358333333333333

4 = (1 - (1 / (1 + 0.00358333333333333))^n) / 0.00358333333333333

4 * 0.00358333333333333 = 1 - (1 / (1 + 0.00358333333333333))^n

0.0143333333333333 = 1 - (1 / (1 + 0.00358333333333333))^n

0.0143333333333333 = 1 - 0.996429461097733^n

Rearrange, we have:

0.996429461097733^n = 1 - 0.0143333333333333

0.996429461097733^n = 0.985666666666667

Loglinearize both sides, we have:

n * log(0.996429461097733) = log(0.985666666666667)

n * (-0.00155344030551834) = -0.00626993019354464

n = -0.00626993019354464 / -0.00155344030551834

n = 4.03615779201283 = 4.04

Therefore, Ramon will pay off his loan within 4.04 months.

For Stephen:

PV = Present value of loan = $1,200

P = Monthly payments = $300

r = Monthly interest rate = 2.4% / 12 = 0.024 / 12 = 0.002

n = number of months = ?

Substitute the values into equation (1) and solve for n, we have:

1,200 = 300 * ((1 - (1 / (1 + 0.002))^n) / 0.002)

1,200 / 300 = (1 - (1 / (1 + 0.002))^n) / 0.002

4 = (1 - (1 / (1 + 0.002))^n) / 0.002

4 * 0.002 = 1 - (1 / (1 + 0.00358333333333333))^n

0.008 = 1 - (1 / (1 + 0.002))^n

0.008 = 1 - 0.998003992015968^n

Rearrange, we have:

0.998003992015968^n = 1 - 0.008

0.998003992015968^n = 0.992

Loglinearize both sides, we have:

n * log(0.998003992015968) = log(0.992)

n * (-0.000867721531226935) = -0.00348832784582135

n = -0.00348832784582135 / -0.000867721531226935 = 4.02010059712238 = 4.02

Therefore, Stephen will pay off his loan within 4.02 months.

(c) Both men would likely get a better interest rate if they used a credit card, rather than a personal loan, to make their purchases.

This is a likely occurence, not a fact, as both Ramon and Stephen have not actually chose to used a credit card. Therefore, it is not possible to know whether it is true or not.

(d) If Ramon applies to Stephen's bank, instead, for his loan, he's guaranteed to get the same 2.4% interest rate that Stephen's been offered.

This is a conditional statement that may be true or not. Therefore, cannot be verified to determine whether it is true or not since Ramon has not actually applied to Stephen's bank.

Summary

The following facts can be obtained from the above:

Ramon's monthly payments = $35.59

Stephen's monthly payments is $34.58

Number of months Ramon will pay off his loan = 4.04 months

Number of months Stephen will pay off his loan = 4.02 months

Conclusion

Based on the summary above, the first statement is true. That is, it is true that if each loan has a term of 3 years, Ramon's monthly payments will be higher. This is because Ramon’s monthly payments of $35.59 is higher than Stephen's monthly payments of $34.58.

yes the total will be same because in both of them the expression.is rearranged but their sign remains the same hence it hss just been shuffled

6. 104

7. 52/37

8. 2704

9. 140608

10. -52

11. |52|=52

12. 1/52

13. 156

14. 26

15. 40

16. 37

17. -364

18. 53 1/3

19. 50.96

20. 43 2/3

21. 78

22. 50.75

23. 47.63

24. 163.28

25. 10400

26. 338

27. 208

28. 2704 square inches

29. 312 square meters

30. don't know what its asking, tell me so i can tell you

31. 8490.56

32. 52 degrees would be an acute angle

33. 128 degrees

34. 20.8

35. 39

36. 208