fixed installment loan of $13,500 with 60 months to pay back, monthly payments of $280.24. instead of making 36th payment, pays remaining balance on loan. how much interest saved? use acturial method u= n*p*v/100+v
To calculate the interest saved on a fixed installment loan, we first need to find the original interest amount for the full 60-month term.
The formula you've provided, u = (n * p * v) / (100 + v), calculates the original interest amount. Here's how to apply it:
1. Determine the loan amount (p): In this case, the loan amount is $13,500.
2. Determine the loan term (n): The loan term is 60 months.
3. Determine the monthly payment (v): The monthly payment is $280.24.
Now let's substitute the values into the formula:
u = (60 * $280.24 * $13,500) / (100 + $280.24)
Calculating the expression within the brackets first:
u = (60 * $280.24 * $13,500) / (100 + $280.24)
u = $22,809,600 / 380.24
u ≈ $60,002.32
So the original interest amount for the 60-month loan is approximately $60,002.32.
Now, if the remaining balance is paid off before the 36th payment, we need to calculate the new interest amount for the remaining payments.
To do this, subtract the remaining balance from the original loan amount ($13,500) and calculate the new monthly payment:
New loan amount = $13,500 - Remaining balance
The remaining balance is the amount that would have been paid in the remaining 24 payments (after the 36th payment). Given the original monthly payment of $280.24, the remaining balance would be:
Remaining balance = 24 * $280.24
Once you have the remaining balance, find the new monthly payment using the remaining balance and the remaining term (24 months).
Finally, calculate the new interest amount using the formula mentioned earlier:
u = (24 * New monthly payment * Remaining balance) / (100 + New monthly payment)
Subtract the new interest amount from the original interest amount to find out how much interest is saved.