Respuesta :
The loan option that would allow Charles to pay the LEAST in interest is option A.
What is Compound Interest?
Compound Interest is a process where the interest is credited to the initial amount and interest, on the whole, is charged again. and this continues for t period of time.
It is given by the formula,
[tex]A=P(1+r\%)^n[/tex]
where A is the value after t period of time, P is the principal amount, and,
r is the rate of interest.
A.) Principle amount = $10,000
Time Period of loan = 2 years
Rate of Interest = 4.75% per annum
Now, the total amount can be written as
[tex]=P(1+r\%)^n\\\\= \$10,000 \times (1+0.0475)^2\\\\= \$10,972.56[/tex]
The interest will be = $10,972.56 - $10,000 = $972.56
B.) Principle amount = $10,000
Time Period of loan = 3 years
Rate of Interest = 4.00% per annum
Now, the total amount can be written as
[tex]=P(1+r\%)^n\\\\= \$10,000 \times (1+0.04)^2\\\\= \$11,248.64[/tex]
The interest will be = $11,248.64 - $10,000 = $1,248.64
C.) Principle amount = $10,000
Time Period of loan = 4 years
Rate of Interest = 3.75% per annum
Now, the total amount can be written as
[tex]=P(1+r\%)^n\\\\= \$10,000 \times (1+0.0375)^2\\\\= \$11,586.5[/tex]
The interest will be = $11,586.5- $10,000 = $1,586.5
D.) Principle amount = $10,000
Time Period of loan = 5 years
Rate of Interest = 3.00% per annum
Now, the total amount can be written as
[tex]=P(1+r\%)^n\\\\= \$10,000 \times (1+0.03)^5\\\\= \$11,592.74[/tex]
The interest will be = $11,592.74 - $10,000 = $1,592.74
Hence, the loan option that would allow Charles to pay the LEAST in interest is option A.
Learn more about Compound Interest:
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