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.
The final amount of the college fund is ___ and the amount of interest gained is $___
To find the final amount of the college fund, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Final amount
P = Principal amount (initial deposit)
r = Annual interest rate (as a decimal)
n = Number of times the interest is compounded per year
t = Number of years
In this case, the principal amount (P) is $5,000, the annual interest rate (r) is 7.3% or 0.073 as a decimal, the interest is compounded monthly (n = 12), and the number of years (t) is 18.
Plugging in the values, we get:
A = 5000(1 + 0.073/12)^(12*18)
Calculating this, we find:
A ≈ $14,760.47
So, the final amount of the college fund is approximately $14,760.47.
To find the amount of interest gained, we can subtract the principal amount from the final amount:
Interest = A - P
Interest = $14,760.47 - $5,000
Interest ≈ $9,760.47
Therefore, the amount of interest gained is approximately $9,760.47.
are you sure? what's the answer?
I apologize for any confusion. Let me recalculate the answer.
The correct formula for compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = Final amount
P = Principal amount (initial deposit)
r = Annual interest rate (as a decimal)
n = Number of times the interest is compounded per year
t = Number of years
In this case, the principal amount (P) is $5,000, the annual interest rate (r) is 7.3% or 0.073 as a decimal, the interest is compounded monthly (n = 12), and the number of years (t) is 18.
Plugging in the values, we get:
A = 5000(1 + 0.073/12)^(12*18)
Calculating this, we find:
A ≈ $19,286.10
So, the final amount of the college fund is approximately $19,286.10.
To find the amount of interest gained, we can subtract the principal amount from the final amount:
Interest = A - P
Interest = $19,286.10 - $5,000
Interest ≈ $14,286.10
Therefore, the amount of interest gained is approximately $14,286.10.