Suppose that you have an outstanding loan that requires ten annual payments of $$2300.$ Now is Year $0$ and the next payment on the loan is due next year, i$.$e$.,$ in Year $1.$ The last payment is due in Year $10.$ There is a bank account that offers a $5\%$ annual interest rate. You would like to make a deposit into this account today $($i$.$e$.,$ in Year $0)$ that would allow you to repay this loan.

$($a$)$ What is the amount you need to deposit?

$($b$)$ Demonstrate that the amount you deposited is enough to repay the loan. $($Recall the mortgage schedule excel we used in the case study.$)$