Suppose that you borrow $10,000
for three
years at 7%
toward the purchase of a car. Use PMT equals StartStartFraction Upper P left parenthesis StartFraction r Over n EndFraction right parenthesis OverOver left bracket 1 minus left parenthesis 1 plus StartFraction r Over n EndFraction right parenthesis Superscript negative nt right bracket EndEndFraction
to find the monthly payments and the total interest for the loan.
To solve this problem, we need to understand the PMT formula for loan calculation:
PMT = P * (r/n) / (1 - (1 + r/n)^-nt)
Where:
P = principal amount (the amount of the loan)
r = annual interest rate (in decimal form)
n = number of compounding periods per year
t = time (duration of the loan in years)
In this case:
P = $10,000
r = 7% (or 0.07 in decimal form)
n = 12 (monthly payments)
t = 3
Substituting these values into the formula, we get:
PMT = 10000 * (0.07/12) / (1 - (1 + 0.07/12) ^ -(12*3))
This simplifies to:
PMT = $308.77 (rounded to nearest cent)
This means that the monthly payment for the car loan will be approximately $308.77.
As for the total interest, we can calculate it as follows:
Total interest = Total amount paid - Principal
Total amount paid = PMT * n * t
Total amount paid = $308.77 * 12 * 3 = $11115.72
Therefore, the total interest = $11115.72 - $10000 = $1115.72
Hence we can conclude that the monthly repayment for the car loan will be approximately $308.77 and the total interest paid over three years will be approximately $1115.72.
To find the monthly payments and the total interest for the loan, we will use the PMT formula:
PMT = P * (r / n) / (1 - (1 + r / n)^(-nt))
Where:
P = Principal (Loan amount) = $10,000
r = Annual interest rate = 7% = 0.07
n = Number of compounding periods per year = 12 (assuming monthly payments)
t = Number of years = 3
Let's calculate the monthly payments first:
PMT = 10,000 * (0.07 / 12) / (1 - (1 + 0.07 / 12)^(-12 * 3))
PMT = $308.63 (approximate monthly payment)
Now let's find the total interest paid over the loan term:
Total Interest = (PMT * 12 * 3) - P
Total Interest = (308.63 * 12 * 3) - 10,000
Total Interest = $3,509.68 (approximate total interest paid)
Therefore, the monthly payment for the loan is approximately $308.63, and the total interest paid is approximately $3,509.68.