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. (1 point)
The final amount of the college fund is $ and the amount of interest gained is $
To solve this problem, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount ($5,000)
r = the annual interest rate (7.3% or 0.073)
n = the number of times the interest is compounded per year (12 since it's compounded monthly)
t = the number of years (18)
Plugging in the values, we get:
A = 5000(1 + 0.073/12)^(12*18)
A ≈ 5000(1 + 0.00608)^(216)
A ≈ 5000(1.00608)^216
A ≈ 5000(2.747422)
A ≈ 13,737.11
Therefore, the final amount of the college fund is $13,737.11.
To calculate the interest gained, we subtract the principal amount from the final amount:
Interest = A - P
Interest ≈ 13,737.11 - 5000
Interest ≈ 8,737.11
Therefore, the amount of interest gained is $8,737.11.