in the picture thanks a bunch yall 6. (6p) You need to purchase a car, but don't have the money to buy it outright. Therefore, you’ll have toborrow money for a loan. Your current situation is this:• The car you want to buy costs $11,999• You have $5500 saved for a down payment on the car.• The dealer offers add-on interest loans for 7% per year, for 1, 3, or 5 years.• You want to keep your car payments under $250 per month.(a) Calculate the monthly payments for 1, 3, or 5 years. Can you afford any of these loan terms?Explain.(b) Compute the total interest you'll pay over the life of each loan.

Answered: 6. (6p) You need to purchase a car, but…

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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in the picture thanks a bunch yall

6. (6p) You need to purchase a car, but don't have the money to buy it outright. Therefore, you’ll have to
borrow money for a loan. Your current situation is this:
• The car you want to buy costs $11,999
• You have $5500 saved for a down payment on the car.
• The dealer offers add-on interest loans for 7% per year, for 1, 3, or 5 years.
• You want to keep your car payments under $250 per month.
(a) Calculate the monthly payments for 1, 3, or 5 years. Can you afford any of these loan terms?
Explain.
(b) Compute the total interest you'll pay over the life of each loan.

Expert Solution

Step 1 What is installments?

Installments are the amount of periodic payments the borrower needs to pay to the lender in order to pay back his loan.

$I n s t a l l m e n t s = P \times r \times [\frac{{(1 + r)}^{n}}{{(1 + r)}^{n} - 1}]$

P = principal amount

r = rate of interest

n = number of periods

Step 2 Calculating installment

a) According to the question, we need to calculate the installment amount in each of the loan terms and evaluate the affordability of the car.

Case 1: loan term is 1 year

$P r i n c i p a l a m o u n t = C o s t o f c a r - d o w n p a y m e n t P r i n c i p a l a m o u n t = $ 11, 999 - $ 5, 500 P r i n c i p a l a m o u n t = $ 6, 499 M o n t h l y r a t e = \frac{7 %}{12} M o n t h l y r a t e = 0.5833 % N u m b e r o f p e r i o d s = 1 y e a r \times 12 m o n t h n u m b e r o f p e r i o d s = 12 P u t t i n g t h e v a l u e s, I n s t a l l m e n t s = $ 6, 499 \times 0.005833 \times [\frac{{(1 + 0.005833)}^{12}}{{(1 + 0.005833)}^{12} - 1}] I n s t a l l m e n t s = $ 6, 499 \times 0.005833 \times [\frac{1.072289654}{0.072289654}] I n s t a l l m e n t s = $ 6, 499 \times 0.005833 \times [14.83323816] I n s t a l l m e n t s = $ 562.30$

The monthly installment in case of 1 years loan will be $562.30

Case2: loan term is 3 year

$P r i n c i p a l a m o u n t = C o s t o f c a r - d o w n p a y m e n t P r i n c i p a l a m o u n t = $ 11, 999 - $ 5, 500 P r i n c i p a l a m o u n t = $ 6, 499 M o n t h l y r a t e = \frac{7 %}{12} M o n t h l y r a t e = 0.5833 % N u m b e r o f p e r i o d s = 3 y e a r \times 12 m o n t h n u m b e r o f p e r i o d s = 36 P u t t i n g t h e v a l u e s, I n s t a l l m e n t s = $ 6, 499 \times 0.005833 \times [\frac{{(1 + 0.005833)}^{36}}{{(1 + 0.005833)}^{36} - 1}] I n s t a l l m e n t s = $ 6, 499 \times 0.005833 \times [\frac{1.232910878}{0.232910878}] I n s t a l l m e n t s = $ 6, 499 \times 0.005833 \times [5.293487745] I n s t a l l m e n t s = $ 200.66$

The monthly installment in case of 3 years loan will be $200.66

Case 3: loan term is 5 year

$P r i n c i p a l a m o u n t = C o s t o f c a r - d o w n p a y m e n t P r i n c i p a l a m o u n t = $ 11, 999 - $ 5, 500 P r i n c i p a l a m o u n t = $ 6, 499 M o n t h l y r a t e = \frac{7 %}{12} M o n t h l y r a t e = 0.5833 % N u m b e r o f p e r i o d s = 5 y e a r \times 12 m o n t h n u m b e r o f p e r i o d s = 60 P u t t i n g t h e v a l u e s, I n s t a l l m e n t s = $ 6, 499 \times 0.005833 \times [\frac{{(1 + 0.005833)}^{60}}{{(1 + 0.005833)}^{60} - 1}] I n s t a l l m e n t s = $ 6, 499 \times 0.005833 \times [\frac{1.417622441}{0.417622441}] I n s t a l l m e n t s = $ 6, 499 \times 0.005833 \times [3.394507339] I n s t a l l m e n t s = $ 128.68$

The monthly installment in case of 5 years loan will be $128.68

CONCLUSION

YES, the borrower can afford loan terms of 3 and 5 years, because he wants to keep the loan installment less than $250 per month. His monthly payments will be less than $250 in both cases.

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