Respuesta :
Answer:
b. $97.25
Step-by-step explanation:
Your number sense tells you a loan of this duration will have a monthly payment not much greater than $5000/60 ≈ $83. Of the offered answer choices, $97.25 is the most reasonable guess.
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If you work this out using a financial calculator, it will tell you the monthly payment is $97.25.
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Additional comment
As a first approximation, the interest paid on an amortized loan is about half of the simple interest amount. We can guess at the monthly payment by computing the payment on a simple interest loan at half the rate.
The total due on a $5000 loan at 3.125% interest is ...
A = P(1 +rt) = 5000(1 +5(0.03125)) = 5000(1.15625) = 5781.25
If 1/60 of that is paid each month, the payment is about $96.35. This guess is within 10% of the actual payment value. With suitable approximations, you can do this calculation without a calculator.
The monthly payment for the loan amount with interest rate which compounded monthly is 97.25. Option B is correct option.
What is compound interest?
Compound interest is the amount charged on the principal amount and the accumulated interest with a fixed rate of interest for a time period.
The formula for the final amount with the monthly compound interest formula can be given as,
[tex]A=P\left(1+\dfrac{R}{100n}\right)^{nt}[/tex]
Here, (A) is the final amount (principal plus interest amount) on the principal amount of (P) with the rate of (r) in the time period of (t). Also, (n) is the number of months.
The principal amount of the loan is $5000.
The interest rate of the loan amount is 6.25% and the total number of months is 60.
First found the discount factor as,
[tex]D=1+\dfrac{(1+\dfrac{6.25}{12\times100})^{-60}}{\dfrac{6.25}{100\times12}}\\D=51.415[/tex]
Monthly payment is the ratio of total loan amount to the discount factor. Thus, monthly payment is,
[tex]M_p=\dfrac{5000}{51.415}\\M_p\cong97.247[/tex]
Thus the monthly payment for the loan amount with interest rate which compounded monthly is 97.25. Option B is correct option.
Learn more about the compound interest here;
https://brainly.com/question/24274034
