Answer :
[tex]\frac{10.25}{100}[/tex]Answer:
Step-by-step explanation:
The formula for simple interest is: A= P(1+in)
The formula for compound interest is: A=P[tex](1+i)^{n}[/tex]
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 +[tex]\frac{10.25}{100}[/tex] ×7)
=0
b) A=2 000 (1 + [tex]\frac{10.25}{100}[/tex] ×7)
A=3435
c) A= 3 000( 1 + [tex]\frac{10.25}{100}[/tex] ×7)
A= 5152.5
d) 5000(1 + [tex]\frac{10.25}{100}[/tex] ×7)
= 8587.5
It's just a matter of substitution. I hope this helped.
Answer:
(a) $668.39
(b) $634.93
(c) $618.20
(d) $584.74
Step-by-step explanation:
Monthly Payment Formula
[tex]\sf PMT=\dfrac{Pi\left(1+i\right)^n}{\left(1+i\right)^n-1}[/tex]
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
[tex]\implies \sf PMT=\dfrac{39950\left(\dfrac{0.1025}{12}\right)\left(1+\left(\dfrac{0.1025}{12}\right)\right)^{84}}{\left(1+\left(\dfrac{0.1025}{12}\right)\right)^{84}-1}[/tex]
[tex]\implies \sf PMT = 668.3892086[/tex]
Therefore, the monthly payment is $668.39.
Part (b)
Down payment = $2,000
⇒ P = $39,950 - $2,000 = $37,950
[tex]\implies \sf PMT=\dfrac{37950\left(\dfrac{0.1025}{12}\right)\left(1+\left(\dfrac{0.1025}{12}\right)\right)^{84}}{\left(1+\left(\dfrac{0.1025}{12}\right)\right)^{84}-1}[/tex]
[tex]\implies \sf PMT = 634.9279215[/tex]
Therefore, the monthly payment is $634.93.
Part (c)
Down payment = $3,000
⇒ P = $39,950 - $3,000 = $36,950
[tex]\implies \sf PMT=\dfrac{36950\left(\dfrac{0.1025}{12}\right)\left(1+\left(\dfrac{0.1025}{12}\right)\right)^{84}}{\left(1+\left(\dfrac{0.1025}{12}\right)\right)^{84}-1}[/tex]
[tex]\implies \sf PMT = 618.197278[/tex]
Therefore, the monthly payment is $618.20.
Part (d)
Down payment = $5,000
⇒ P = $39,950 - $5,000 = $34,950
[tex]\implies \sf PMT=\dfrac{34950\left(\dfrac{0.1025}{12}\right)\left(1+\left(\dfrac{0.1025}{12}\right)\right)^{84}}{\left(1+\left(\dfrac{0.1025}{12}\right)\right)^{84}-1}[/tex]
[tex]\implies \sf PMT = 584.735991[/tex]
Therefore, the monthly payment is $584.74.
