What is the future worth of P6oo deposited at the end of every month for 4 years if the interest rate is 12% compounded quarterly?
To find the future worth of P600 deposited at the end of every month for 4 years with a 12% interest rate compounded quarterly, we can break down the problem into smaller steps.
Step 1: Calculate the total number of deposits.
Since the deposit was made at the end of every month for 4 years, we multiply the number of years (4) by the number of months in a year (12):
Total number of deposits = 4 years * 12 months/year = 48 deposits
Step 2: Determine the interest rate per period.
Since the interest rate is given as 12% compounded quarterly, we divide the annual interest rate (12%) by the number of compounding periods in a year (4):
Interest rate per period = 12% / 4 = 3%
Step 3: Calculate the future worth of each deposit.
To find the future worth of each deposit, we can use the formula for the future value of a series of equal periodic payments:
FV = P * [(1 + r)^n - 1] / r
Where:
FV = Future value of the deposit
P = Amount of each deposit (P600 in this case)
r = Interest rate per period (3% in this case)
n = Number of periods (48 deposits in this case)
Plugging in the values, we get:
FV = P * [(1 + r)^n - 1] / r
= 600 * [(1 + 0.03)^48 - 1] / 0.03
Step 4: Calculate the future worth of all deposits.
To find the future worth of all deposits, we multiply the future worth of each deposit by the total number of deposits:
Total future worth = FV * Total number of deposits
Plugging in the values, we get:
Total future worth = FV * 48
Now you can calculate the future worth of P600 deposited at the end of every month for 4 years with a 12% interest rate compounded quarterly by substituting the values into the formulas and performing the calculations.