Summary
Highlights
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.
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.
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.
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.
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.
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 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.
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.
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.
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.
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.