00:00The final amount is $13,310, and the total compound interest earned is $3,310,
00:07calculated using A equals P, 1 plus R, carat N equals 10,000 times, 1.10, carat 3.
00:16This assumes standard annual compounding with no withdrawals or additional deposits during the
00:22three-year term. Breaking it down year by year clarifies why compounding beats simple interest.
00:27Year 1 ends at $11,000, plus $1,000. Year 2 at $12,100, plus $1,100. And year 3
00:38at $13,310,
00:41plus $1,210. Each year's interest grows because it's calculated on the previous year's total,
00:47not just the original principle. With simple interest at the same rate, you'd only reach $13,000,
00:53a $310 difference that becomes far more significant over longer periods or higher
00:59principles. The compounding frequency changes the result meaningfully. 1. Annual compounding,
01:05N equals 3, R equals 10%, $13,310, the baseline case above. 2. Semiannual compounding, R equals 5%
01:16per period, N equals $13,400.96, about $91 more, since interest is applied twice yearly. 3. Monthly
01:27compounding, R is almost equal to 0.833% per period, N equals 36 approximately $13,481.80, roughly $172
01:40more than
01:40annual. The highest of the three because interest compounds most frequently. The answer changes
01:46depending on context. If this is a bank deposit or loan, always check whether the stated rate is
01:52nominal annual or effective annual, since financial institutions often advertise nominal rates while
01:58compounding monthly or daily, which increases actual returns slash costs beyond the simple formula
02:04above. For investment products, factor in fees and taxes, which aren't included in this calculation
02:10and can reduce net returns significantly. Practical takeaway. Use A equals P, 1 plus or slash N,
02:18caret, and T, rather than the basic annual formula whenever you're comparing real financial products,
02:24and always confirm the compounding frequency stated in the contract or account terms before relying on
02:30projected figures. This single detail can shift outcomes by hundreds of dollars over just a few
02:36years. Finally, remember that everything we discussed today is for educational purposes only
02:41and does not constitute financial advice. Good luck to everyone, and see you in the next video.
