Determine the accrued interest amount of a $5,000 student loan with a simple interest rate of 5.4% over a period of 8 years. Round the answer to two decimal places as needed.
What is the accrued interest amount?
To find the accrued interest amount, we can use the formula: Accrued Interest = Principal x Rate x Time.
The principal is $5,000.
The rate is 5.4% or 0.054 as a decimal.
The time is 8 years.
Plugging these values into the formula, we get: Accrued Interest = $5,000 x 0.054 x 8 = $2,160.
Therefore, the accrued interest amount is $2,160.
To prepare for retirement, Chris invests $15,000 with a simple interest rate of 4.8%. Find the final amount of Chris's investment if he invests this amount for the next 30 years. Round the answer to two decimal places as needed.
What is the final amount of Chris's investment?
To find the final amount of Chris's investment, we can use the formula: Final Amount = Principal + Accrued Interest.
The principal amount is $15,000.
The rate is 4.8% or 0.048 as a decimal.
The time is 30 years.
Plugging these values into the formula, we get: Final Amount = $15,000 + ($15,000 x 0.048 x 30).
Calculating the expression in the parentheses first, we have: Final Amount = $15,000 + ($15,000 x 1.44).
Multiplying $15,000 by 1.44, we get $21,600.
Adding this to the principal amount, the final amount of Chris's investment is: Final Amount = $15,000 + $21,600 = $36,600.
Therefore, the final amount of Chris's investment is $36,600.
Anne invests $7,000 into a retirement account with a compound interest rate of 3.3% compounded quarterly. What is Anne's final amount after 25 years of investment? Round the answer to the nearest cent.
To find the final amount, we can use the formula for compound interest:
Final Amount = Principal * (1 + Rate/Compounding Frequency)^(Compounding Frequency * Time)
The principal amount is $7,000.
The rate is 3.3% or 0.033 as a decimal.
The compounding frequency is quarterly, which means it compounds 4 times a year.
The time is 25 years.
Plugging these values into the formula, we get:
Final Amount = $7,000 * (1 + 0.033/4)^(4 * 25)
Calculating the expression in parentheses first, we have:
Final Amount = $7,000 * (1 + 0.00825)^(100)
We can simplify 1 + 0.00825 to 1.00825.
Final Amount = $7,000 * 1.00825^(100)
Calculating 1.00825 raised to the power of 100, we get approximately 2.10159.
Final Amount = $7,000 * 2.10159
Multiplying $7,000 by 2.10159, we get approximately $14,710.13.
Therefore, Anne's final amount after 25 years of investment is approximately $14,710.13.
Serenity wants to invest $25,000 of her savings for her retirement fund. Determine the difference in interest earnings between a 10% simple interest rate and a 7% compound interest rate with interest being compounded annually if Serenity invests her money for 25 years. Round the answer to two decimal places as needed.
The difference in interesting earnings is what?
To find the difference in interest earnings, we need to calculate the interest earned under the simple interest rate and compound interest rate, and then subtract the simple interest from the compound interest.
For simple interest:
Principal = $25,000
Rate = 10% or 0.10 as a decimal
Time = 25 years
Simple Interest = Principal x Rate x Time = $25,000 x 0.10 x 25 = $62,500
For compound interest:
Principal = $25,000
Rate = 7% or 0.07 as a decimal
Time = 25 years
Compound Interest = Principal * (1 + Rate)^Time - Principal = $25,000 * (1 + 0.07)^25 - $25,000
Using a calculator, we find that (1 + 0.07)^25 is approximately 3.869684.
Compound Interest = $25,000 * 3.869684 - $25,000 = $96,742.10 - $25,000 = $71,742.10
To find the difference in interest earnings, we subtract the simple interest from the compound interest:
Difference in Interest Earnings = Compound Interest - Simple Interest = $71,742.10 - $62,500 = $9,242.10
Therefore, the difference in interest earnings is $9,242.10.