How to Solve Sinking Fund Problems
Solve sinking fund aptitude problems using the future value of an annuity formula, a worked example, and detailed practice questions.
Expected Interview Answer
A sinking fund is a series of equal periodic deposits, each earning compound interest, that accumulates to a target future amount, so the required deposit is found by solving A = D × [((1+r)^n − 1) / r] for D, where D is the deposit, r is the periodic rate, and n is the number of deposits.
Unlike a single lump-sum compound interest problem, a sinking fund involves repeated deposits at regular intervals, each of which compounds for a different remaining duration until the target date — the first deposit compounds the longest, the last deposit barely compounds at all. Summing these individually compounded deposits produces a geometric series, which collapses into the future value of an annuity formula, A = D × [((1+r)^n − 1) / r]. Given the target amount A, rate r, and number of periods n, you solve for the required periodic deposit D = A×r / ((1+r)^n − 1). Sinking funds are used to retire debt, replace equipment, or fund a known future liability without needing a single large payment at the end.
- Converts a scary “save up to a target” problem into one annuity formula
- Distinguishes sinking-fund (many deposits) from lump-sum compounding (one deposit)
- Directly applicable to real financial planning: debt retirement, replacement funds
AI Mentor Explanation
A young batter aiming to reach 10,000 career runs does not need one giant innings — small consistent contributions across many matches, each adding to a growing career tally that itself gains value (reputation, sponsorship) the earlier it was built, accumulate toward the target. A sinking fund works identically: instead of one lump-sum deposit, equal periodic deposits each compound for their own remaining time until the target date, and A = D×[((1+r)^n − 1)/r] sums all those individually-compounded contributions into the final goal.
Worked example
Annuity factor
- ((1.10)^4 − 1)/0.10
- = 4.641
Required deposit
- D = 50000/4.641
- ≈ 10,774
Check
- 4 deposits of 10,774, compounded
- ≈ 50,000 at year 4
Step-by-Step Explanation
Step 1
Identify A, r, and n
Target future amount A, periodic rate r, and number of equal deposits n.
Step 2
Apply the annuity future-value formula
A = D × [((1+r)^n − 1) / r], the sum of n individually-compounding deposits.
Step 3
Solve for the unknown
Rearrange to D = A×r / ((1+r)^n − 1) when the required deposit is the unknown.
Step 4
Match compounding frequency to deposit frequency
Ensure r and n use the same period length (e.g. both annual, or both monthly).
What Interviewer Expects
- Correct distinction between a sinking fund (repeated deposits) and lump-sum compounding (one deposit)
- Accurate use of the annuity future-value formula and its rearrangement for D
- Matching the compounding period to the deposit interval consistently
- Recognizing real-world sinking fund use cases like debt retirement or equipment replacement
Common Mistakes
- Treating a sinking fund as simple interest instead of compound annuity growth
- Using a lump-sum compound interest formula instead of the annuity future-value formula
- Mismatching deposit frequency and compounding frequency (e.g. monthly deposits with an annual rate)
- Forgetting that the last deposit contributes little to no interest, since it compounds for almost no time
Best Answer (HR Friendly)
“A sinking fund is a series of equal deposits, made regularly, each earning compound interest until a target date — rather than one big lump-sum payment. The total accumulated amount is the future value of an annuity, A = D times the annuity factor ((1+r)^n minus 1) over r, so you rearrange that formula to solve for the deposit size D needed to hit your target A.”
Follow-up Questions
- How would the formula change if deposits were made at the start of each period instead of the end?
- How do you find the number of deposits needed given a fixed deposit amount and target?
- How does a sinking fund differ from an amortizing loan repayment schedule?
- How would you compute the fund balance partway through the deposit schedule, not just at the end?
MCQ Practice
1. A sinking fund needs to reach 26,620 in 3 years with annual deposits at 10% per annum. The approximate annual deposit is?
D = A×r/((1+r)^n − 1) = 26620×0.10/((1.10)^3 − 1) = 2662/0.331 ≈ 8,047.
2. In a sinking fund, which deposit contributes the LEAST accumulated interest by the target date?
The last deposit compounds for the shortest remaining time before the target date, so it earns the least interest.
3. The future value of a sinking fund with equal deposits D, rate r, and n periods is given by which formula?
This is the standard future value of an ordinary annuity formula, summing all individually-compounding deposits.
Flash Cards
What is a sinking fund? — A series of equal periodic deposits, each compounding, that accumulate to a target future amount.
Future value of a sinking fund formula? — A = D × [((1+r)^n − 1) / r].
Formula to find required deposit D? — D = A × r / ((1+r)^n − 1).
Which deposit earns the least interest? — The last deposit, since it compounds for the shortest remaining time.