How to Solve Loans and Sinking Funds — Loans — sinking-fund method: deposit, periodic outlay, total interest cost Questions on Exam FM

Exam FM Topic: Loans and Sinking Funds — Loans — sinking-fund method: deposit, periodic outlay, total interest cost Verified Procedural Question
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 \(X\).
(A)2846.9192
(B)2763.9992
(C)2692.3058
(D)2174.7934
(E)1897.9461
📖 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 \(2846.92\).
Therefore, the result is \(\frac{7070863716590336460200000000000000000000000000000000000000000000000000000 a}{68122318582951682301 \left(\left(a + 100\right)^{25} - 100000000000000000000000000000000000000000000000000\right)}\approx 2846.9192\), so the correct answer is option (A).

Final Answer: Option (A)

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