Summary
Highlights
This example focuses on 'discounting' 25,000 pesos at 12% compounded monthly for five years, which means finding the present value (P). The calculation involves using the present value formula, with 'i' and 'n' determined by the given rates and compounding period.
The video introduces the compound interest formula, explaining how to calculate both the future amount (F) using the compound amount formula F = P(1+i)^n and the present value (P) using the formula P = F(1+i)^-n. It defines new variables such as 'j' for nominal rate per year and 'm' for the frequency of conversion. 'i' is calculated as j/m, and 'n' as t*m, where 't' is time in years.
The term (1+i)^n is identified as the accumulation factor, and (1+i)^-n as the discount factor. The video then explains the values for 'm' (frequency of conversion) based on how often interest is compounded: annually (m=1), semi-annually (m=2), quarterly (m=4), and monthly (m=12).
The first example demonstrates finding the compound amount for an investment of 50,000 pesos at 8% compounded quarterly for four years. The steps involve calculating 'i' (j/m) and 'n' (t*m) and then substituting these values into the compound amount formula.
This example shows how to 'accumulate' 12,000 pesos at 9% compounded semi-annually for two years. This again involves finding the future value (F), following the same logical steps of calculating 'i' and 'n' and then applying the compound amount formula.
Ferdinand wants to have 80,000 pesos in three years. This example calculates how much he needs to invest today (P) in a bank paying 9% compounded monthly, using the present value formula.
Mirna deposited 450,000 pesos at 14% compounded quarterly. This example calculates how much she can withdraw after four years and two months, requiring the conversion of months into a decimal of a year for 't'.
Cindy wants 1.5 million in five years and two months. This final example determines how much she should deposit now (P) at a bank offering 12% compounded quarterly, again involving conversion of months to a decimal of a year for 't' and applying the present value formula.