Question

If no payments are made, a loan of amount $23000 would increase to $26079.89 after 2 years of monthly compounding interest. If instead, payments of $384.44 are made at the end of each month, how many years would it be until the loan is paid off?

Answer 1

To calculate the number of years it would take to pay off the loan with monthly payments, we can use the present value of annuity formula.

Step-by-step explanation:

To find out how many years it would take to pay off the loan, we need to calculate the monthly payment required to pay off the loan in a certain number of years. Let's assume the loan will be paid off in x years.

Using the formula for the present value of an annuity:

PV = R[(1 - (1 + i)^(-n)) / i]

Where PV is the loan amount, R is the monthly payment, i is the monthly interest rate, and n is the number of months.

For the given loan amount of $23,000, the monthly payment of $384.44, and the interest rate, we can solve for n:

$23,000 = $384.44[(1 - (1 + i)^(-12x)) / i]

This equation can be solved using numerical methods or trial and error to find the value of x.