Payments of $1690 at the end of every six months will pay off the balance owed on a loan in 9.5 years.
If the interest rate on the loan is 9.9% compounded semiannually, what is the current balance on the loan? (Do not round intermediate calculations and round your final answer to 2 decimal places.)
To find the current balance on the loan, we can use the formula for the present value of an ordinary annuity:
PV = PMT * (1 - (1 + r)^(-n)) / r
Where:
PV = present value (or current balance) of the loan
PMT = payment per period ($1690)
r = interest rate per period (9.9% compounded semiannually = 4.95% per period)
n = number of periods (9.5 years = 19 periods)
Plugging in the values into the formula:
PV = $1690 * (1 - (1 + 4.95%)^(-19)) / 4.95%
Now, let's calculate this:
PV = $1690 * (1 - (1.0495)^(-19)) / 0.0495
PV ≈ $1690 * (1 - 0.340322) / 0.0495
PV ≈ $1690 * 0.659678 / 0.0495
PV ≈ $11,320.71
Therefore, the current balance on the loan is approximately $11,320.71.