When Martin was born, his father set up a $5,000 college fund for him with an annual compound interest rate of 7.3%. What is the final amount of the final amount of this college fund, and how much interest is gained if this fund is invested for 18 years if interest is compounded monthly?
Round the answers to two decimal places as needed.
The final amount of the college fund is $____, and the amount of interest gained is $____.
To calculate the final amount of the college fund, we can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
Where:
A = the final amount of the college fund
P = the initial principal amount ($5000)
r = annual interest rate (7.3% or 0.073)
n = number of times interest is compounded per year (12 monthly)
t = number of years (18)
Plugging in the given values, we have:
A = 5000(1 + 0.073/12)^(12*18)
A = 5000(1.00608333333)^(216)
A ≈ $15,159.12
So, the final amount of the college fund is approximately $15,159.12.
To calculate the amount of interest gained, we subtract the initial principal amount from the final amount:
Interest = A - P
Interest = $15,159.12 - $5000
Interest ≈ $10,159.12
Therefore, the amount of interest gained is approximately $10,159.12.