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 β 5000(1 + 0.00608)^(216)
A β 5000(1.00608)^216
A β 5000(2.747422)
A β 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 β 13,737.11 - 5000
Interest β 8,737.11
Therefore, the amount of interest gained is $8,737.11.