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 solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal (initial amount)
r = the annual interest rate (in decimal form)
n = the number of times interest is compounded per year
t = the number of years
In this case, the principal is $5,000, the annual interest rate is 7.3% or 0.073 in decimal form, the interest is compounded monthly (n = 12), and the investment period is 18 years.
Plugging in these values, we get:
A = 5000(1 + 0.073/12)^(12*18)
Calculating this expression, we find:
A ≈ 5000(1 + 0.006083)^216
A ≈ 5000(1.006083)^216
A ≈ 5000(2.446872)
A ≈ 12,234.36
So, the final amount of the college fund is $12,234.36
To find the amount of interest gained, we subtract the principal from the final amount:
Interest = A - P
Interest = 12,234.36 - 5000
Interest ≈ 7234.36
So, the amount of interest gained is approximately $7,234.36.