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)
wrong, its 6220.03 for the final amount, and for the interest it is 120.02.
Apologies for the incorrect answer. Let me recalculate the values for you.
Using the same formula as before:
A = P(1 + r/n)^(nt)
With the given values:
P = $5,000
r = 7.3% or 0.073 as a decimal
n = 12 (monthly compounding)
t = 18 years
A = 5000(1 + 0.073/12)^(12*18)
A ≈ 5000(1 + 0.006083333)^216
A ≈ 5000(1.006083333)^216
A ≈ 5000 * 2.259910484
A ≈ $11,299.55
Therefore, the final amount of the college fund is approximately $11,299.55.
To find the amount of interest gained, we subtract the principal amount from the final amount:
Interest = A - P
Interest ≈ $11,299.55 - $5,000
Interest ≈ $6,299.55
Therefore, the amount of interest gained is approximately $6,299.55.
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 = the final amount
P = the principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times that 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), the number of times interest is compounded per year is 12 (monthly compounding), and the number of years is 18. Plugging in these values into the formula, we get:
A = 5000(1 + 0.073/12)^(12*18)
A ≈ 5000(1 + 0.006083333)^216
A ≈ 5000(1.006083333)^216
A ≈ 5000 * 2.713560389
A ≈ $13,567.80
Therefore, the final amount of the college fund is approximately $13,567.80.
To find the amount of interest gained, we subtract the principal amount from the final amount:
Interest = A - P
Interest ≈ $13,567.80 - $5,000
Interest ≈ $8,567.80
Therefore, the amount of interest gained is approximately $8,567.80.