Summary
Highlights
Example 3: Loan Repayment Calculation00:15:51
Chris borrows 50,000 pesos at 12% compounded monthly and needs to know the total amount to repay after six years. Using the formula, the future value is calculated as 102,354.97 pesos.
Formula for Present Value00:20:23
The formula for finding the present value (P) at compounded interest is presented: P = F / (1 + r/m)^(m*t) or P = F / (1 + i)^n, where F is the future value.
Introduction to Compound Interest More Than Once a Year00:00:10
This video lesson discusses compound interest when it is compounded more than once a year. Objectives include computing interest, maturity value, and present value, and solving related problems.
Key Definitions and Terms00:00:37
Key terms defined are: frequency of conversion (m), conversion of interest periods (t), total number of conversion periods (n = m * t), nominal rate (r), and interest rate for each conversion period (i = r/m). Examples of 'm' values include 1 for annually, 2 for semi-annually, 4 for quarterly, and 12 for monthly.
Calculating Interest Rate Per Period and Frequency of Conversion00:03:01
The video illustrates how to calculate the frequency of conversion (m) and the interest rate per period (i) for different compounding frequencies (annually, semi-annually, quarterly, monthly, daily) given a nominal rate of two percent.
Formula for Maturity Value (Future Value)00:06:38
The formula for calculating maturity value (F) or future value when compounded m times a year is introduced: F = P * (1 + r/m)^(m*t) or F = P * (1 + i)^n, where P is the principal, r is the nominal rate, t is the time in years, m is the frequency of conversion, i is the interest rate per period, and n is the total number of conversion periods.
Example 1: Calculating Maturity Value and Interest (Quarterly)00:07:53
An example demonstrates finding the maturity value and interest for a 10,000 pesos deposit at 2% compounded quarterly for five years. The calculation uses the formula F = P * (1 + i)^n and results in a future value of 11,048.96 pesos and an interest of 1,048.96 pesos.
Example 2: Calculating Maturity Value and Interest (Monthly)00:12:15
This example calculates the maturity value and interest for the same 10,000 pesos deposit at 2% but compounded monthly for five years. The future value is found to be 11,050.79 pesos, and the interest is 1,050.79 pesos.
Example 1: Calculating Present Value (Semi-Annually)00:21:13
An example shows how to find the present value of 50,000 pesos due in four years, invested at 12% compounded semi-annually. The present value is calculated to be 31,370.62 pesos.
Example 2: Calculating Present Value (Quarterly)00:23:25
This example calculates the present value of 25,000 pesos due in two years and six months, with money worth 10% compounded quarterly. The present value is determined to be 19,529.96 pesos.
Quiz Time: Test Your Knowledge00:26:08
A five-question quiz is presented to test understanding of the concepts covered, including frequency of conversion, nominal rates, conversion periods, and interest rates in different compounding scenarios.