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 use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = final amount
P = principal amount (original investment)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case, the principal amount is $5,000, the annual interest rate is 7.3% (or 0.073 as a decimal), and interest is compounded monthly (n = 12). The investment period is 18 years (t = 18).
Using the formula:
A = 5000(1 + 0.073/12)^(12*18)
Calculating this expression, the final amount of the college fund is $15,143.36.
To find the amount of interest gained, we subtract the principal amount from the final amount:
Interest = A - P = $15,143.36 - $5000 = $10,143.36
Therefore, the final amount of the college fund is $15,143.36, and the amount of interest gained is $10,143.36.