You have an investment of $100 with an interest rate of 5%, with a total of three compounding periods. Every end of the year is considered a period. Calculate the compounding value of the investment at the end of the three periods.
Answer (1)
To calculate the compounding value of an investment, you can use the formula for compound interest:
A = P ( 1 + n r ) n t
where:
A is the amount of money accumulated after n years, including interest.
P is the principal amount (initial investment).
r is the annual interest rate (decimal).
n is the number of times that interest is compounded per year.
t is the time the money is invested for in years.
In this problem, the investment is $100 with an interest rate of 5% and three compounding periods at the end of each year. This implies:
P = 100
r = 0.05
n = 1 (since it is compounded annually)
t = 3
Substituting these values into the formula gives:
A = 100 ( 1 + 1 0.05 ) 1 × 3 = 100 ( 1 + 0.05 ) 3 = 100 × 1.0 5 3
Calculating further:
A = 100 × 1.157625 = 115.7625
Therefore, the compounding value of the investment at the end of the three periods is approximately $115.76.
