determine the accrued interest and the final amount of an $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
To calculate the accrued interest, we use the formula:
Accrued Interest = Principal * Rate * Time
Accrued Interest = $10,000 * 0.0475 * 13 = $6,175
To find the final amount, we simply add the accrued interest to the principal:
Final Amount = Principal + Accrued Interest = $10,000 + $6,175 = $16,175
Therefore, the accrued interest is $6,175 and the final amount is $16,175.
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. (1 point)
The final amount of the
investment after 27 years is $ _____
To calculate the final amount of the investment, we use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = Final amount
P = Principal (initial investment)
r = Annual interest rate (in decimal form)
n = Number of times interest is compounded per year
t = Number of years
Given:
P = $15,000
r = 3.4% = 0.034 (decimal form)
n = 4 (quarterly compounding)
t = 27 years
Plugging in the values into the formula:
A = $15,000(1 + 0.034/4)^(4*27)
A = $15,000(1.0085)^(108)
Using a calculator, we find:
A ≈ $15,000(2.07474218092) = $31,120.13
Therefore, the final amount of the investment after 27 years, compounded quarterly, is approximately $31,120.13.
Are you sure
Apologies for the mistake. Let me recalculate.
The correct formula for compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = Final amount
P = Principal (initial investment)
r = Annual interest rate (in decimal form)
n = Number of times interest is compounded per year
t = Number of years
Given:
P = $15,000
r = 3.4% = 0.034 (decimal form)
n = 4 (quarterly compounding)
t = 27 years
Plugging in the values into the formula:
A = $15,000(1 + 0.034/4)^(4*27)
A = $15,000(1.0085)^(108)
Using a calculator, we find:
A ≈ $15,000(2.69862553309) = $40,479.38 (rounded to the nearest cent)
Therefore, the final amount of the investment after 27 years, compounded quarterly, is approximately $40,479.38.