Preview
IB DP Mathematics: Applications and Interpretation | SL & HL | Number and Algebra — Topic 1.4
📋 Learning Intentions
- Calculate the future value of an investment or loan using the compound interest formula, identifying each parameter correctly.
- Apply the TVM Solver on the TI-84 Plus CE to solve compound interest, depreciation, and annuity problems.
- Find the real value of an investment by adjusting for inflation using the real interest rate.
- Determine the depreciated value of an asset using both the reducing-balance and straight-line depreciation models.
- Interpret the effect of compounding frequency on the growth of an investment and distinguish nominal from effective annual rates.
- Justify financial decisions by comparing the real value of money over time, accounting for both interest and inflation.
Real-World Introduction
Suppose a student deposits $5 000 into a savings account at age 18. By age 65, without ever adding another cent, that deposit could grow to over $100 000 — not because of magic, but because of compounding. Each year, interest is earned not just on the original deposit but on all previously accumulated interest. This self-reinforcing growth is the engine behind long-term wealth accumulation and the reason financial advisers consistently emphasise starting early.
The same mathematics that grows savings also shrinks them. A car purchased for $30 000 may be worth only $12 000 after four years of depreciation. A government bond paying 4% annual interest sounds attractive — until inflation is running at 5%, meaning the purchasing power of the investment is actually falling. Understanding compound interest, depreciation, and real value allows students to evaluate financial products critically rather than accepting headline figures at face value.
🌍 Why This Matters Central banks, mortgage lenders, pension funds, and car dealerships all use compound interest models daily. The IB formula booklet entry for compound interest is the same formula used by every bank in the world to calculate loan repayments and savings growth — mastering it gives students a genuine tool for real financial decisions.
Core Concepts & Definitions
When money is invested, the simplest model assumes interest is paid only on the original principal — this is simple interest. In practice, however, banks and financial institutions calculate interest on the accumulated total, including previously earned interest. This process, repeated over multiple periods, produces compound interest.
📖 Key Definition — Compound Interest Compound interest is interest calculated on both the initial principal and the interest accumulated from previous periods. The future value \( FV \) after \( n \) compounding periods is given by: \[ FV = PV \left(1 + \frac{r}{100k}\right)^{kn} \] where \( PV \) is the present value (principal), \( r \) is the nominal annual interest rate as a percentage, \( k \) is the number of compounding periods per year, and \( n