Similar with simple interest, computations for the principal amount anticipates the expected or planned future amount would be paying or received. However, it is not easy to determine the principal to be invested or borrowed due to the compounding manner of applying the interest.
Using the formula for computing the future amount, the formula for calculating the principal can be derived. This would be
Principal ` = text(Future Amount)/(1+ text(Rate per Period))^text(Number of Periods)`
Future amount is $10,000.
Rate of interest is 4% compounded semiannually.
Determining the number of years;
18 – 10 = 8 years
Determining the rate of interest per period;
Rate per Period ` = text(Nominal Rate)/text(Periods per Year)`
Note: Semiannually means every 6 months and therefore, there are 2 periods per year.
Rate per Period ` = (4%)/( 2) = 2%`
Determining the number of periods;
Number of Periods = Periods per Year x Number of Years
Number of Periods = 2 x 8
Number of Periods = 16
Using the formula for solving the principal;
Principal = `text(Future Amount)/(1+ text(Rate per Period))^text(Number of Periods)`
Principal = `text($10,000)/(1 + 0.02)^16 `
Principal = `text($10,000)/(1.02)^16`
Principal = `text($10,000)/1.3728`
Principal = `$7,284.46`
Therefore, the father must invest $7,284.46 in the bank.
Future amount is $15,000,000.
Rate of interest is 6% compounded monthly.
Number of years is 10.
The price of the lot is the principal.
Determining the rate of interest per period;
Rate per Period ` = text(Nominal Rate)/text(Periods per Year)`
Note: There are 12 periods in a year since there are 12 months in a year.
Rate per Period ` = (6%)/( 12) = 0.5%`
Number of Periods = Periods per Year x Number of Years
Number of Periods = 12 x 10
Number of Periods = 120
Using the formula for solving the principal;
Principal = `text(Future Amount)/(1+ text(Rate per Period))^text(Number of Periods)`
Principal = `text($15,000,000)/(1 + 0.005)^120 `
Principal = `text($15,000,000)/(1.005)^120`
Principal = `text($15,000,000)/1.8194`
Principal = `$8,244,491.00`
Therefore, the price of the lot was $8,244,491.00.
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