Question

D) $39,950

8. The car is $39,950. Interest is 10.25% and you finance for 7 years.
Figure the payments if you put down a) $0 b) $2,000 c) $3,000 d)
$5,000

Answer 1

`(10.25)/(100)`Answer:

Explanation:

The formula for simple interest is: A= P(1+in)

The formula for compound interest is: A=P
`(1+i)^(n)`

A= amount after added interest

P= initial amount invested

i= interest rate

n= number of periods (in this case its 7 years)

*REMEMBER THIS FORMULA

a) A=0

P=?

i=10,25

n=7

(simple interest)

a) A= 0 (1 +
`(10.25)/(100)` ×7)

=0

b) A=2 000 (1 +
`(10.25)/(100)` ×7)

A=3435

c) A= 3 000( 1 +
`(10.25)/(100)` ×7)

A= 5152.5

d) 5000(1 +
`(10.25)/(100)` ×7)

= 8587.5

It's just a matter of substitution. I hope this helped.

Answer 2

(a) $668.39

(b) $634.93

(c) $618.20

(d) $584.74

Explanation:

Monthly Payment Formula

`\sf PMT=(Pi\left(1+i\right)^n)/(\left(1+i\right)^n-1)`

where:

• PMT = monthly payment.
• P = loan amount.
• i = interest rate per month (in decimal form).
• n = term of the loan (in months).

Given:

• P = $39.950 less any down payment.
• i = 10.25% / 12 = 0.1025/12
• n = 7 years = 7 × 12 = 84 months

Part (a)

Down payment = $0

⇒ P = $39,950

`\implies \sf PMT=(39950\left((0.1025)/(12)\right)\left(1+\left((0.1025)/(12)\right)\right)^(84))/(\left(1+\left((0.1025)/(12)\right)\right)^(84)-1)`

`\implies \sf PMT = 668.3892086`

Therefore, the monthly payment is $668.39.

Part (b)

Down payment = $2,000

⇒ P = $39,950 - $2,000 = $37,950

`\implies \sf PMT=(37950\left((0.1025)/(12)\right)\left(1+\left((0.1025)/(12)\right)\right)^(84))/(\left(1+\left((0.1025)/(12)\right)\right)^(84)-1)`

`\implies \sf PMT = 634.9279215`

Therefore, the monthly payment is $634.93.

Part (c)

Down payment = $3,000

⇒ P = $39,950 - $3,000 = $36,950

`\implies \sf PMT=(36950\left((0.1025)/(12)\right)\left(1+\left((0.1025)/(12)\right)\right)^(84))/(\left(1+\left((0.1025)/(12)\right)\right)^(84)-1)`

`\implies \sf PMT = 618.197278`

Therefore, the monthly payment is $618.20.

Part (d)

Down payment = $5,000

⇒ P = $39,950 - $5,000 = $34,950

`\implies \sf PMT=(34950\left((0.1025)/(12)\right)\left(1+\left((0.1025)/(12)\right)\right)^(84))/(\left(1+\left((0.1025)/(12)\right)\right)^(84)-1)`

`\implies \sf PMT = 584.735991`

Therefore, the monthly payment is $584.74.