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 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 amount ($5,000)
r = annual interest rate (7.3% or 0.073)
n = number of times interest is compounded per year (12 for monthly)
t = number of years (18)
Plugging in these values:
A = 5000(1 + 0.073/12)^(12*18)
Using a calculator, we can find:
A ≈ $16,894.38
Therefore, the final amount of the college fund is approximately $16,894.38.
To calculate the amount of interest gained, we can subtract the initial amount from the final amount:
Interest = A - P = $16,894.38 - $5,000 = $11,894.38
Therefore, the amount of interest gained is $11,894.38.