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
To solve this, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Final amount after time t
P = Initial principal (in this case, $5,000)
r = Annual interest rate (in decimal form, 7.3% = 0.073)
n = Number of times interest is compounded per year (12, since it's compounded monthly)
t = Number of years (18)
Plugging in these values, we get:
A = 5000(1 + 0.073/12)^(12*18)
Using a calculator, we can evaluate this expression:
A ≈ 5000(1 + 0.00608416667)^(216)
A ≈ 5000(1.00608416667)^(216)
A ≈ 5000(2.38425845076)
A ≈ 11921.29
So, the final amount of the college fund is approximately $11,921.29.
To find the amount of interest gained, we subtract the initial principal from the final amount:
Interest = Final amount - Initial principal
Interest = $11,921.29 - $5,000
Interest ≈ $6,921.29
Therefore, the gain in interest is approximately $6,921.29.