And here we go again – I mean those ugly formulas from financial mathematics 🙂 We can already calculate how much our deposit will earn interest (Future value) or, conversely, how much we initially deposited if our target amount is XYZ USD (Present value). We can create a repayment schedule in Excel and calculate an annuity payment in Excel using PMT function. Everyone should know how to do that, right? But we still don’t know how to save, or more precisely, calculate regular deposits so that we accumulate a certain amount over time – for that, we have a friend from financial mathematics => Sinking Fund Factor
Let’s look at another practical situation many people face. If we want to save – regularly set aside some amount, for example into a savings account – we can easily calculate using financial mathematics:
How much to regularly set aside in a savings account (or other product) to reach a desired amount after a certain period – for example, 1,000,000 USD for a trip around the world?
Sinking Fund Factor (Saving) – Formula and Explanation – How much to save regularly?
Where:
- FV = balance at the end of the period (after n periods) = future value
- Regular deposit = the amount we will regularly deposit for a given number of periods
- i = interest rate
- n = number of periods
- The expression i/[(1+i)n -1] is Sinking fund factor
Sinking fund factor with an Excel Saving Example
Example Problem: Suppose we are 40 years old and want to enjoy a trip around the world in retirement (say in 30 years), which will cost 1,000,000 USD. We want to regularly (annually) deposit money into a bank product with a compound interest rate of 2% p.a. How much must we save annually to reach the target amount in 30 years?
Solution:
To save 1 million USDin 30 years at 2% p.a. interest and be able to go on the trip, we would need to make an annual deposit of 24,650 USD. But beware of inflation! (see below)…
Sinking fund factor and Accounting for Inflation – So We Are Not Surprised…
In 30 years, our regular deposits will not have the same value as when we put them in the bank due to the Time Value of Money effect. In other words, if the trip costs 1 million USD today, it will cost more in 30 years. Correctly, we should include at least inflation (ideally other risks too). The steps would be:
- Estimate the inflation rate (e.g., 2% p.a.), which annually reduces purchasing power, and use the compounding factor to calculate the Future Value (FV). The exact future inflation rate is unknown, but we know it will occur – we can at least estimate it. For example, using predictions from the Central bank authority or our own judgment.
- Plug this inflation adjusted FV into the Sinking factor formula
Conclusion: If we account for 2% inflation, we will need 1,811,362 USD (in compare to 1 mil USD) in 30 years for the trip, meaning the annual deposit should be much higher >> 44,649 USD.
Advanced Financial Modeling and Time Value of Money
In advanced financial modeling (corporate environment), which considers the Time Value of Money, we try to account not only for interest rate and inflation but also other factors. This applies, for example, to investment evaluation (IRR) or loan interest rates. These factors are quantified using various mathematical approaches with market data. This is relevant for discount rate determination, WACC (Weighted Average Cost of Capital), etc., including:
- Credit risk (non-zero risk that a business entity could go bankrupt within 30 years) – derived from the company’s rating if covered by a rating agency or otherwise
- Liquidity risk (investment temporarily reduces solvency, and costs from this risk are expressed via a risk premium)
- Opportunity costs
- And more
Discount rates, WACC, and investment evaluation methods will be discussed another time.