How to Solve Loans and Sinking Funds — Loans — sinking-fund method: deposit, periodic outlay, total interest cost Questions on Exam FM
Sample Practice Problem
ID: #FLBO5
A participant makes equal deposits \(X\) at the end of each year for \(25\) years into the municipal archive preservation program, earning \(3\%\) annually. Immediately after the last deposit, the entire balance purchases a \(15\)-payment annuity-immediate paying \(10,000\) annually, priced at \(5\%\). Calculate \(X\).
📖 Worked Solution & Strategy
At the purchase date the deposits have accumulated to \(X s_{25|0.030}\), while the annuity costs \(10,000a_{15|0.050}\). Equating these values gives \[X=\frac{10,000a_{15|0.050}}{s_{25|0.030}}=2846.9192.\] Therefore each year-end deposit is \(2846.92\).