Jane has a $35,000 bank loan that she wishes to pay off in five equal annual payments with 12% interest. If the first payment is due one year from today, what will be the amount of the annual payment necessary
61,682
To calculate the amount of the annual payment necessary to pay off a bank loan, you can use the formula for the present value of an ordinary annuity:
PV = P * (1 - (1 + r)^(-n)) / r
Where:
PV = Present Value (loan amount)
P = Annual payment
r = Interest rate per period (in this case, per year)
n = Number of periods (in this case, the number of years)
In this case, Jane has a $35,000 bank loan that she wants to pay off in five equal annual payments with a 12% interest rate.
Let's plug the values into the formula:
PV = $35,000
r = 0.12 (12% expressed as a decimal)
n = 5
Now, we need to solve for P, which represents the annual payment.
1. First, rearrange the formula to solve for P:
P = PV * r / (1 - (1 + r)^(-n))
2. Substitute the given values:
P = $35,000 * 0.12 / (1 - (1 + 0.12)^(-5))
3. Calculate the result to find the annual payment amount:
P ≈ $10,119.98
Therefore, Jane needs to make annual payments of approximately $10,119.98 to pay off her $35,000 bank loan in five equal payments with a 12% interest rate.