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.
Would answers 18,531.23 and 6,570 be correct?
To calculate the final amount of the college fund, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the initial amount (in this case, $5,000)
r = the annual interest rate (7.3% or 0.073)
n = the number of times interest is compounded per year (12, for monthly compounding)
t = the number of years (18)
Plugging in the values, we have:
A = 5000(1 + 0.073/12)^(12*18)
A ≈ 5000(1 + 0.0060833)^(216)
A ≈ 5000(1.0060833)^216
A ≈ 5000 * 4.01588272
A ≈ 20,079.41
Therefore, the final amount of the college fund after 18 years is approximately $20,079.41.
To calculate the interest gained, we can subtract the initial amount from the final amount:
Interest gained = A - P
Interest gained ≈ 20,079.41 - 5000
Interest gained ≈ 15,079.41
Therefore, the interest gained from investing the college fund for 18 years is approximately $15,079.41.
So the correct answers would be $20,079.41 and $15,079.41, not $18,531.23 and $6,570.