Find the balance after 10 years of a $30,000 savings account that pays 10% interest compounded yearly.(1 point)
Responses
$33,154.81
$33,154.81
$77,812.27
$77,812.27
$2,245,256.05
$2,245,256.05
$112,070.90
Using the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = annual nominal interest rate (in decimal form)
n = number of times that interest is compounded per year
t = number of years the money is invested or the loan is taken out for
In this case:
P = $30,000 (principal amount)
r = 10% (0.10 in decimal form)
n = 1 (compounded yearly)
t = 10 (10 years)
Plugging in the values:
A = $30,000(1 + 0.10/1)^(1*10)
A = $30,000(1 + 0.10)^10
A = $30,000(1.10)^10
A = $30,000(2.5937)
A ≈ $77,812.27
So, the correct answer is:
$77,812.27
Between simple interest at 8% and compound interest at 9%, find the higher resulting balance after investing $500 for a period of 10 years. Round the answer to two decimal places.(1 point)
The higher resulting balance after investing $500 for a period of 10 years is $
To calculate the future balance using simple interest, we use the formula:
A = P(1 + rt)
Where:
A = the future value of the investment
P = the principal investment amount (the initial deposit)
r = annual interest rate (in decimal form)
t = number of years the money is invested for
In this case:
P = $500 (principal amount)
r = 8% (0.08 in decimal form)
t = 10 (10 years)
Using the formula:
A = $500(1 + 0.08*10)
A = $500(1 + 0.8)
A = $500(1.8)
A = $900
So, after 10 years with simple interest at 8%, the balance would be $900.
To calculate the future balance using compound interest, we use the formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal investment amount (the initial deposit)
r = annual nominal interest rate (in decimal form)
n = number of times that interest is compounded per year
t = number of years the money is invested for
In this case:
P = $500 (principal amount)
r = 9% (0.09 in decimal form)
n = 1 (compounded yearly)
t = 10 (10 years)
Using the formula:
A = $500(1 + 0.09/1)^(1*10)
A = $500(1 + 0.09)^10
A = $500(1.09)^10
A = $500(2.3674)
A ≈ $1,183.70
So, after 10 years with compound interest at 9%, the balance would be $1,183.70.
Therefore, the higher resulting balance after investing $500 for a period of 10 years is $1,183.70.
Aria is investing $6,700 of her savings from her summer job for her college fund. She is planning to invest the amount for 3 years and can choose between simple interest at 6.5% and compound interest at 6%. Find the difference between the two interest earning types to help Aria decide which investing option is best for her.(1 point)
Responses
Aria should invest with 6% compound interest because it will result in $86.76 more in interest earnings.
Aria should invest with 6% compound interest because it will result in $86.76 more in interest earnings.
Aria should invest with 6% compound interest because it will result in $73.81 more in interest earnings.
Aria should invest with 6% compound interest because it will result in $73.81 more in interest earnings.
Aria should invest with 6.5% simple interest because it will result in $187.26 more in interest earnings.
Aria should invest with 6.5% simple interest because it will result in $187.26 more in interest earnings.
Aria should invest with 6.5% simple interest because it will result in $26.69 more in interest earnings.
To find the difference between the two interest earning types, we need to calculate the interest earned by each option and then subtract the amount earned with simple interest from the amount earned with compound interest.
For the option of simple interest at 6.5%:
I = P * r * t
Where:
I = interest earned
P = principal amount (initial deposit)
r = annual interest rate (in decimal form)
t = number of years the money is invested for
In this case:
P = $6,700 (principal amount)
r = 6.5% (0.065 in decimal form)
t = 3 (3 years)
Using the formula:
I = $6,700 * 0.065 * 3
I = $1,302.50
So, with simple interest at 6.5%, Aria would earn $1,302.50 in interest.
For the option of compound interest at 6%:
A = P * (1 + r/n)^(nt) - P
Where:
A = future value of the investment (including interest)
P = principal amount (initial deposit)
r = annual nominal interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years the money is invested for
In this case:
P = $6,700 (principal amount)
r = 6% (0.06 in decimal form)
n = 1 (compounded yearly)
t = 3 (3 years)
Using the formula:
A = $6,700 * (1 + 0.06/1)^(1*3) - $6,700
A = $6,700 * (1 + 0.06)^3 - $6,700
A = $6,700 * (1.06)^3 - $6,700
A ≈ $7,040.86 - $6,700
A ≈ $340.86
So, with compound interest at 6%, Aria would earn approximately $340.86 in interest.
Now, we can calculate the difference:
Difference = Amount earned with compound interest - Amount earned with simple interest
Difference = $340.86 - $1,302.50
Difference ≈ -$961.64
The negative difference indicates that Aria would earn more interest with simple interest at 6.5% than with compound interest at 6%. Thus, the correct answer is:
Aria should invest with 6.5% simple interest because it will result in $961.64 more in interest earnings.