Compound interest: yearly, half-yearly or quarterly
Put money in a fixed deposit at a bank. Change the principal, the rate, the time and how often interest is added, and compare the compound interest with simple interest.
Core concept
With interest added k times a year, the compound amount is A = P(1 + R/100k)^(kT); the more often it is added, the more interest earns interest
Topic: Compound interest
In simple interest, interest is paid only on the principal: SI = PRT/100. In compound interest, the interest is added to the principal at the end of each period, and the next interest is worked out on the new, bigger amount: interest earns interest. Added once a year, the compound amount after T years is A = P(1 + R/100)^T. Added half-yearly, the rate for each half year is R/2 and there are 2T periods: A = P(1 + R/200)^(2T). Added quarterly, A = P(1 + R/400)^(4T). Compound interest is CI = A − P.
What you will learn
- Calculate the yearly compound amount and compound interest.
- Calculate half-yearly and quarterly compound interest.
- Compare compound interest with simple interest.
Before you start
- Know simple interest, SI = PRT/100.
Materials
- A notebook and a calculator
Equipment
- None
Procedure
- Record Rs 50000 at 10% for 2 years, added yearly.
- Change to half-yearly and record.
- Change to quarterly and record.
- Make the time 3 years and record.
How this simulation is simplified
- No money is added or taken out during the time, and there is no tax on the interest.