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)^(nt)
Where:
A = the final amount
P = the principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
In this problem:
P = $5,000
r = 7.3% (or 0.073 as a decimal)
n = 12 (compounded monthly)
t = 18 years
Plugging in these values, we can calculate the final amount:
A = 5000(1 + 0.073/12)^(12*18)
A ≈ $14,108.18
Therefore, the final amount of the college fund is approximately $14,108.18.
To calculate the interest gained, we can subtract the principal amount from the final amount:
Interest = A - P
Interest = $14,108.18 - $5,000
Interest ≈ $9,108.18
Therefore, the amount of interest gained is approximately $9,108.18.