Summary
Highlights
The video introduces Mathematics of Investments, outlining topics like interest, annuities, depreciation, and bonds. The first topic is interest, defined as money paid for the use of borrowed money. It distinguishes between simple interest (paid only on the principal) and compound interest (interest calculated on the principal plus accumulated interest).
The simple interest formula is introduced as I = P * R * T, where I is simple interest, P is the principal amount, R is the rate of interest (as a decimal), and T is the time in years. The future amount (F) is also defined as F = P + I, which can be further expressed as F = P * (1 + R * T) or P = F / (1 + R * T).
An example demonstrates calculating the interest earned when Venus deposits 5000 pesos at 6.5% simple interest for two years. Using the formula, the interest earned is 650 pesos.
Another example illustrates finding the interest rate (R) when Christian invested 30,000 pesos and earned 6,500 pesos interest after three years. The calculated rate is 6.22%.
This example shows how to calculate the length of time (T) Lena used borrowed money. With a 10,000 peso loan at 12% simple interest, she paid 4,500 pesos interest, indicating she used the money for 3.75 years.
Rachel paid 7,400 pesos in interest for a loan at 14.5% over four years. The example demonstrates calculating the original loan amount (P), which is 12,758.62 pesos.
Vincent borrowed 35,000 pesos at 12.5% simple interest for five years. This example calculates the future amount (F) he will pay back, which is 56,875 pesos.
Rose borrowed 40,000 pesos at 10.5% simple interest for 15 months. The example demonstrates converting months to years and calculating the future amount she will pay, which is 47,512.50 pesos.
The total amount paid on a loan was 84,000 pesos for two years at 9% simple interest. This final example calculates the original loan amount (P) to be 71,186.44 pesos.