The accrued interest can be calculated using the simple interest formula:
Accrued Interest = Principal * Rate * Time
Principal = $10,000
Rate = 4.75% = 0.0475
Time = 13 years
Accrued Interest = $10,000 * 0.0475 * 13
Accrued Interest = $6,175
The final amount of the investment can be calculated by adding the accrued interest to the principal:
Final Amount = Principal + Accrued Interest
Final Amount = $10,000 + $6,175
Final Amount = $16,175
Therefore, the accrued interest is $6,175 and the final amount of the investment is $16,175.
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 answer to two decimal places as needed.
The accrued interest is $____ and the final amount of the investment is $____
11 answers
Did you round the answers to two decimal places?
Apologies for not rounding the answers.
The accrued interest rounded to two decimal places is $6,175.00.
The final amount of the investment rounded to two decimal places is $16,175.00.
The accrued interest rounded to two decimal places is $6,175.00.
The final amount of the investment rounded to two decimal places 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 final amount of the investment after 27 years is $____
To calculate the final amount after 27 years with quarterly compounding, we can use the formula for compound interest:
Final Amount = Principal * (1 + (Rate / n))^(n * Time)
In this case:
Principal = $15,000
Rate = 3.4% = 0.034
n = 4 (quarterly compounding)
Time = 27 years
Final Amount = $15,000 * (1 + (0.034/4))^(4 * 27)
Using a calculator, we can evaluate this expression:
Final Amount ≈ $15,000 * (1.0085)^(108)
Final Amount ≈ $15,000 * 1.346853041
Final Amount ≈ $20,202.795615
Rounding this to the nearest cent, the final amount of the investment after 27 years is $20,202.80.
Final Amount = Principal * (1 + (Rate / n))^(n * Time)
In this case:
Principal = $15,000
Rate = 3.4% = 0.034
n = 4 (quarterly compounding)
Time = 27 years
Final Amount = $15,000 * (1 + (0.034/4))^(4 * 27)
Using a calculator, we can evaluate this expression:
Final Amount ≈ $15,000 * (1.0085)^(108)
Final Amount ≈ $15,000 * 1.346853041
Final Amount ≈ $20,202.795615
Rounding this to the nearest cent, the final amount of the investment after 27 years is $20,202.80.
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 is this fund is invested for 18 years if interest is compounded monthly? Round the answer to two decimal places as needed.
The final amount of the college fund id $____, and the amount of interest gained is $____
The final amount of the college fund id $____, and the amount of interest gained is $____
To find the final amount of the college fund after 18 years with monthly compounding, we can use the formula for compound interest:
Final Amount = Principal * (1 + (Rate / n))^(n * Time)
In this case:
Principal = $5,000
Rate = 7.3% = 0.073
n = 12 (monthly compounding)
Time = 18 years
Final Amount = $5,000 * (1 + (0.073/12))^(12 * 18)
Using a calculator, we can evaluate this expression:
Final Amount ≈ $5,000 * (1.0060833333)^(216)
Final Amount ≈ $5,000 * 2.530673194
Final Amount ≈ $12,653.37
Therefore, the final amount of the college fund after 18 years is $12,653.37.
To find the amount of interest gained, we can subtract the principal amount from the final amount:
Interest Gained = Final Amount - Principal
Interest Gained = $12,653.37 - $5,000
Interest Gained = $7,653.37
Therefore, the amount of interest gained in this college fund after 18 years is $7,653.37.
Final Amount = Principal * (1 + (Rate / n))^(n * Time)
In this case:
Principal = $5,000
Rate = 7.3% = 0.073
n = 12 (monthly compounding)
Time = 18 years
Final Amount = $5,000 * (1 + (0.073/12))^(12 * 18)
Using a calculator, we can evaluate this expression:
Final Amount ≈ $5,000 * (1.0060833333)^(216)
Final Amount ≈ $5,000 * 2.530673194
Final Amount ≈ $12,653.37
Therefore, the final amount of the college fund after 18 years is $12,653.37.
To find the amount of interest gained, we can subtract the principal amount from the final amount:
Interest Gained = Final Amount - Principal
Interest Gained = $12,653.37 - $5,000
Interest Gained = $7,653.37
Therefore, the amount of interest gained in this college fund after 18 years is $7,653.37.
What is the final amount of the college fund and the amount of interest gained.
Apologies for the confusion. The final amount of the college fund after 18 years with monthly compounding is $12,699.30.
To calculate the amount of interest gained, we subtract the initial principal from the final amount:
Interest Gained = Final Amount - Principal
Interest Gained = $12,699.30 - $5,000
Interest Gained = $7,699.30
Therefore, the amount of interest gained in this college fund after 18 years is $7,699.30.
To calculate the amount of interest gained, we subtract the initial principal from the final amount:
Interest Gained = Final Amount - Principal
Interest Gained = $12,699.30 - $5,000
Interest Gained = $7,699.30
Therefore, the amount of interest gained in this college fund after 18 years is $7,699.30.
Angel wants to invest $7,000 for 3 years. He has two investing options.
Option 1: Investing with a 15% simple interest rate.
Option 2: Investing with a 12% compound interest rate, with interest being compounded quarterly.
Find the difference in interest earnings to help Angel determine which investing option will give more financial returns.
The difference in interest earnings is $_____, and option _____ is the better investing option.
Option 1: Investing with a 15% simple interest rate.
Option 2: Investing with a 12% compound interest rate, with interest being compounded quarterly.
Find the difference in interest earnings to help Angel determine which investing option will give more financial returns.
The difference in interest earnings is $_____, and option _____ is the better investing option.
To calculate the interest earnings for each option, we can use the following formulas:
Option 1 (Simple Interest):
Interest = Principal * Rate * Time
Option 2 (Compound Interest):
Final Amount = Principal * (1 + (Rate / n))^(n * Time)
Interest = Final Amount - Principal
Option 1:
Principal = $7,000
Rate = 15% = 0.15
Time = 3 years
Interest1 = $7,000 * 0.15 * 3
Interest1 = $3,150
Option 2:
Principal = $7,000
Rate = 12% = 0.12
n = 4 (quarterly compounding)
Time = 3 years
Final Amount2 = $7,000 * (1 + (0.12/4))^(4 * 3)
Final Amount2 ≈ $7,000 * (1.03)^(12)
Final Amount2 ≈ $7,000 * 1.425984
Final Amount2 ≈ $9,981.89
Interest2 = $9,981.89 - $7,000
Interest2 ≈ $2,981.89
To find the difference in interest earnings, we subtract the interest earned with option 1 from the interest earned with option 2:
Difference = Interest2 - Interest1
Difference ≈ $2,981.89 - $3,150
Difference ≈ -$168.11
The difference in interest earnings is approximately -$168.11. This means that option 2, investing with a 12% compound interest rate compounded quarterly, would generate less interest earnings compared to option 1, investing with a 15% simple interest rate.
Therefore, option 1 is the better investing option as it would give more financial returns.
Option 1 (Simple Interest):
Interest = Principal * Rate * Time
Option 2 (Compound Interest):
Final Amount = Principal * (1 + (Rate / n))^(n * Time)
Interest = Final Amount - Principal
Option 1:
Principal = $7,000
Rate = 15% = 0.15
Time = 3 years
Interest1 = $7,000 * 0.15 * 3
Interest1 = $3,150
Option 2:
Principal = $7,000
Rate = 12% = 0.12
n = 4 (quarterly compounding)
Time = 3 years
Final Amount2 = $7,000 * (1 + (0.12/4))^(4 * 3)
Final Amount2 ≈ $7,000 * (1.03)^(12)
Final Amount2 ≈ $7,000 * 1.425984
Final Amount2 ≈ $9,981.89
Interest2 = $9,981.89 - $7,000
Interest2 ≈ $2,981.89
To find the difference in interest earnings, we subtract the interest earned with option 1 from the interest earned with option 2:
Difference = Interest2 - Interest1
Difference ≈ $2,981.89 - $3,150
Difference ≈ -$168.11
The difference in interest earnings is approximately -$168.11. This means that option 2, investing with a 12% compound interest rate compounded quarterly, would generate less interest earnings compared to option 1, investing with a 15% simple interest rate.
Therefore, option 1 is the better investing option as it would give more financial returns.
11 answers