Charles would like to buy a new car that costs $32 000. The dealership offers to finance the car at 2.4%/a compounded monthly for five years with monthly payments. The dealer will reduce the selling price by$3000 if Charles pays cash. Charles can get a loan from his bank at 5.4%/a compounded monthly. Which is the best way to buy the car? Justify your answer with calculations.

Question

04-06-2022
Mathematics

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Charles would like to buy a new car that costs $32 000. The dealership offers to finance the car at 2.4%/a compounded monthly for five years with monthly payments. The dealer will reduce the selling price by$3000 if Charles pays cash. Charles can get a loan from his bank at 5.4%/a compounded monthly. Which is the best way to buy the car? Justify your answer with calculations.

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okpalawalter8 okpalawalter8 · Answer 1 · 2022-06-14T21:08:14+02:00

Charles would like to buy a new car that costs $32 000. The dealership offers to finance the car at 2.4%/a, it's best for Charles loans from the bank to buy car.

Which is the best way to buy a car?

Generally, the equation for the monthly loan payment is mathematically given as

[tex]R=\frac{\frac{iP}{N}}{1-(\frac{1}{N})^{NY}}[/tex]

Therefore

[tex]R=\frac{\frac{0.024*32000}{12}}{1-(\frac{0.024}{12}+1)^{-12*5}}[/tex]

R=566.51

Hence the total payment is

T=R*N*Y

T=33990.34

By taking a loan of 29000, and applying the equation

T'=33155.77

In conclusion, it is best for Charles loans from the bank to buy a car.