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 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 formula to calculate the final amount of a compound interest problem compounded monthly is:
A = P(1 + r/n)^(nt)
Where:
A = Final amount
P = Principal amount (initial investment)
r = Annual interest rate (as a decimal)
n = Number of times that interest is compounded per year
t = Number of years
In this case, Martin's father set up a $5,000 college fund for him with an annual interest rate of 7.3% (or 0.073 as a decimal). The interest is compounded monthly, so n = 12. The investment is made for 18 years, so t = 18.
Plugging these values into the formula:
A = 5000(1 + 0.073/12)^(12*18)
A = 5000(1 + 0.00608)^(216)
A ≈ $15,223.36
Therefore, the final amount of the college fund will be approximately $15,223.36.
To calculate the interest gained, we subtract the principal amount ($5,000) from the final amount ($15,223.36):
Interest = Final amount - Principal amount
Interest = $15,223.36 - $5,000
Interest ≈ $10,223.36
Therefore, the interest gained from this investment over 18 years is approximately $10,223.36.