Determine the accrued interest and the final amount of a $10,000 investment with a 4.75% simple interest rate over a period of 13 years. Round the answers to two decimal places as needed.
The accrued interest is $___ and the final amount of the investment is $___
The formula for simple interest is given by I = PRT, where I is the accrued interest, P is the principal amount, R is the interest rate, and T is the time period.
Using this formula, we can calculate the accrued interest as:
I = 10,000 * 0.0475 * 13 = $6,175.00
To find the final amount, we add the accrued interest to the principal amount:
Final amount = 10,000 + 6,175 = $16,175.00
Therefore, the accrued interest is $6,175.00 and the final amount of the investment is $16,175.00.
Chris invests $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.
The final amount of the investment after 27 years is $___
The formula for compound interest is given by the formula A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the time period in years.
Using this formula, we can calculate the final amount as:
A = 15000(1 + 0.034/4)^(4*27)
A = 15000(1 + 0.0085)^(108)
A = 15000(1.0085)^108
A ≈ 15000(2.360886)
A ≈ $35,413.29
Therefore, the final amount of the investment after 27 years is approximately $35,413.29.
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 in 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 $____
Using the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the time period in years.
P = $5,000
r = 7.3% = 0.073
n = 12 (interest is compounded monthly)
t = 18
Plugging these values into the formula, we get:
A = 5000(1 + 0.073/12)^(12*18)
A = 5000(1 + 0.00608)^(216)
A ≈ 5000(1.00608)^216
A ≈ $13,460.48
Therefore, the final amount of the college fund is approximately $13,460.48.
To calculate the interest gained, we subtract the principal amount from the final amount:
Interest gained = $13,460.48 - $5,000
Interest gained ≈ $8,460.48
Therefore, the amount of interest gained is approximately $8,460.48.