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 formula to calculate compound interest is:
A = P(1+r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested or borrowed for
Given that:
P = $5,000
r = 7.3% = 0.073 (expressed as a decimal)
n = 12 (monthly compounding)
t = 18
Plugging in the values into the formula:
A = $5,000(1+0.073/12)^(12*18)
Evaluating the expression:
A ≈ $5,000(1.0060833)^(216)
A ≈ $5,000(2.10092672)
A ≈ $10,504.63
Therefore, the final amount of Martin's college fund after 18 years is approximately $10,504.63.
To determine the interest gained, subtract the initial principal amount from the final amount:
Interest = $10,504.63 - $5,000
Interest ≈ $5,504.63
Therefore, the interest gained if the fund is invested for 18 years with monthly compounding is approximately $5,504.63.