formula used : [tex]\sf A = P(1 + \dfrac{r}{n})^{nt}[/tex]
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✔A) A 2-year loan with a 4.75% interest rate compounded annually.
[tex]\hookrightarrow \sf A = 10,000 (1 + \dfrac{4.75\%}{1})^{(1)(2)}[/tex]
[tex]\hookrightarrow \sf A = \$10,972.56[/tex]
B) A 3-year loan with a 4.00% interest rate compounded annually.
[tex]\hookrightarrow \sf A = 10,000 (1 + \dfrac{4.00\%}{1})^{(1)(3)}[/tex]
[tex]\hookrightarrow \sf A = \$11248.64[/tex]
C) A 4-year loan with a 3.75% interest rate compounded annually.
[tex]\hookrightarrow \sf A = 10,000 (1 + \dfrac{3.75\%}{1})^{(1)(4)}[/tex]
[tex]\hookrightarrow \sf A = \$11586.50415[/tex]
D) A 5-year loan with a 3.00% interest rate compounded annually.
[tex]\hookrightarrow \sf A = 10,000 (1 + \dfrac{3.00\%}{1})^{(1)(5)}[/tex]
[tex]\hookrightarrow \sf A = \$ 11592.74074[/tex]
Thus loan of 2-year loan with a 4.75% interest which is compounded annually will allow him to pay the least interest of only $972.56.
The least interest is 972.56 dollars. Then he has to select a 2-year loan with a 4.75% interest rate compounded annually.
Compound interest is the interest on a loan or deposit calculated based on the initial principal and the accumulated interest from the previous period.
We know that the formula for the amount will be
[tex]A = P (1 + r) ^t[/tex]
A = Amount
P = Loan amount
r = rate of interest
t = time
The interest is given as
Interest = A - P
Charles needs a $10,000 loan in order to buy a car.
A) A 2-year loan with a 4.75% interest rate compounded annually. Then the amount will be
[tex]\rm A = 10000(1.0475)^2\\\\A = 10972.56[/tex]
Then the interest will be
Interest = 10972.56 - 10000
Interest = 972.56
The amount of interest is $972.56.
B) A 3-year loan with a 4.00% interest rate compounded annually. Then the amount will be
[tex]\rm A = 10000(1.04)^3\\\\A = 11248.64[/tex]
Then the interest will be
Interest = 11248.64 - 10000
Interest = 1248.64
The amount of interest is $1248.64.
C) A 4-year loan with a 3.75% interest rate compounded annually. Then the amount will be
[tex]\rm A = 10000(1.0375)^4\\\\A = 11586.50[/tex]
Then the interest will be
Interest = 11586.50 - 10000
Interest = 1586.50
The amount of interest is $1586.50.
D) A 5-year loan with a 3.00% interest rate compounded annually. Then the amount will be
[tex]\rm A = 10000(1.03)^5\\\\A = 11592.74[/tex]
Then the interest will be
Interest = 11592.74 - 10000
Interest = 1592.74
The amount of interest is $1592.74.
More about the compound interest link is given below.
https://brainly.com/question/25857212
