I am currently faced with a practice problem for a financial mathematics course, and I would like to verify that I am approaching, the problem correctly (and ultimately that my solution is indeed correct).
The problem is as follows:
A loan of $\$250000$ charging a nominal annual interest rate of $6\%$ convertible monthly is to be repaid via the sinking fund method. If payments are made at the end of each month for ten years and the sinking fund earns a nominal annual rate of $4\%$ convertible monthly, find the total monthly expense for the repayment of this loan.
Here are my thoughts:
- We know the loan size $L = 250,000$ and that there are $10 * 12 = 120$ payment periods.
- We know that the loan charges a nominal rate of $6\%$. Since this is a nominal rate, we divide this by $12$ to get the monthly effective rate of $0.06/12 = 0.005 = 0.5\% $
- The sinking fund nominal interest rate is $4\%$, so the sinking fund’s monthly effective rate is $0.04/12 = 0.00333333... = 0.333333...\%$.
- Thus, the interest paid per period is $iL = (0.005) * (250,000) = \$1250$
- And, the sinking fund deposit per period is $250,000 / s_{n=120, j = 0.3\%} = \$1697.80$.
Thus, the total monthly expense = $Interest Paid + Sinking Fund Deposit = 1250 + 1697.80 = 2947.80$
If anyone would be willing to verify the correctness of this (or suggest an alternative approach), it would be greatly appreciated!
Thanks!