Marcel gives Philip a business loan of $10,000 for 2 years with an annual interest rate of 9%.
What is Philip's monthly payment on the loan, rounded to 2 decimal places?
$456.85
$1030.23
$37.50
$1800.00
A = P r (1+r)^n / [ (1+r)^n -1]
where
A = payment Amount per period
P = initial Principal (loan amount)
r = interest rate per period
n = total number of payments or periods
here n = 24 months
r = .09/12 = 0.0075
(1+r) ^24 = (1.0075)^24 = 1.1964
so
10,000 (.0075)1.1964 / [ .1964]
= 456.87
https://www.calculator.net/amortization-calculator.html?cloanamount=10000&cloanterm=2&cinterestrate=9&printit=0&x=61&y=17
To calculate Philip's monthly payment on the loan, we will use the formula for calculating loan payments:
Monthly Payment = (LoanAmount * MonthlyInterestRate) / (1 - (1 + MonthlyInterestRate) ^ -NumberOfPayments)
Here, the LoanAmount is $10,000, the annual interest rate is 9%, the loan duration is 2 years, and we need to find the monthly payment.
First, we need to calculate the MonthlyInterestRate by dividing the annual interest rate by 12 months:
MonthlyInterestRate = (9% / 100) / 12
= 0.09 / 12
= 0.0075 (rounded to 4 decimal places)
Next, we need to calculate the NumberOfPayments by multiplying the loan duration (2 years) by 12 months:
NumberOfPayments = 2 * 12
= 24
Now, we can substitute the values into the loan payment formula:
Monthly Payment = ($10,000 * 0.0075) / (1 - (1 + 0.0075) ^ -24)
= $75 / (1 - 1.0075 ^ -24)
= $75 / (1 - 0.8241)
= $75 / 0.1759
= $425.98 (rounded to 2 decimal places)
Therefore, Philip's monthly payment on the loan, rounded to 2 decimal places, is $425.98.
None of the options provided match the correct answer.
To calculate Philip's monthly payment on the loan, we can use the formula for the monthly payment on a loan:
Monthly Payment = (P * r * (1+r)^n) / ((1+r)^n - 1)
Where:
P = Principal amount (loan amount) = $10,000
r = Monthly interest rate = Annual interest rate / 12 = 9% / 12 = 0.09 / 12 = 0.0075
n = Number of monthly payments = 2 years * 12 months per year = 24
Let's substitute these values into the formula:
Monthly Payment = (10,000 * 0.0075 * (1+0.0075)^24) / ((1+0.0075)^24 - 1)
Calculating this expression gives us: $456.85
Therefore, Philip's monthly payment on the loan, rounded to 2 decimal places, is $456.85.