Chris invents $15,000 in a retirement account with an annual interest rate of 3.4%. Find the final amount of the investment after 27 years if interest is compounded quarterly.
Round the answer to the nearest cent.
We can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (unknown)
P = the principal amount (initial investment), $15,000
r = annual interest rate (as a decimal), 3.4% = 0.034
n = number of times interest is compounded per year, quarterly = 4
t = number of years, 27
Plugging in the values:
A = 15000(1 + 0.034/4)^(4*27)
Calculating inside the parentheses:
A = 15000(1 + 0.0085)^(108)
Calculating the exponent:
A = 15000(1.0085)^(108)
Calculating (1.0085)^(108):
A = 15000(2.239353801)
Calculating:
A ≈ $33,590.31
Therefore, the final amount of the investment after 27 years, compounded quarterly, is approximately $33,590.31.
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 the college fund, 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.
We can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (unknown)
P = the principal amount (initial investment), $5,000
r = annual interest rate (as a decimal), 7.3% = 0.073
n = number of times interest is compounded per year, monthly = 12
t = number of years, 18
Plugging in the values:
A = 5000(1 + 0.073/12)^(12*18)
Calculating inside the parentheses:
A = 5000(1 + 0.006083333333333333)^(216)
Calculating the exponent:
A = 5000(1.006083333333333333)^(216)
Calculating (1.006083333333333333)^(216):
A ≈ 5000(2.057031978)
Calculating:
A ≈ $10,285.16
Therefore, the final amount of the college fund, after 18 years with monthly compounding, is approximately $10,285.16.
To find the amount of interest gained, we subtract the initial investment from the final amount:
Interest = A - P = $10,285.16 - $5,000 = $5,285.16
Therefore, the interest gained on this investment after 18 years is approximately $5,285.16.