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 $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 $26.69 more in interest earnings. Aria should invest with 6.5% simple interest because it will result in $26.69 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% compound interest because it will result in $86.76 more in interest earnings.
To find the difference between the two interest earning types, we need to calculate the interest earnings for each option.
For 6.5% simple interest, the formula is:
Interest = Principal * Rate * Time
The interest earned with simple interest is:
Interest = $6,700 * 0.065 * 3 = $1,302.50
For compound interest at 6%, we can use the formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount
r = the annual interest rate (as a decimal) = 6% = 0.06
n = the number of times that interest is compounded per year (typically 12 for monthly)
t = the number of years the money is invested for
A = $6,700(1 + 0.06/1)^(1*3)
A = $6,700(1.06)^3
A = $6,700 * 1.191016 = $7,977.35
The interest earned with compound interest is:
Interest = A - P = $7,977.35 - $6,700 = $1,277.35
The difference in interest earnings between the two options is:
$1,302.50 - $1,277.35 = $25.15
So, the correct answer is:
Aria should invest with 6.5% simple interest because it will result in $25.15 more in interest earnings.
Analyze the incentive as shown here to find the total price when two medium one-topping pizzas are purchased with the incentive. “1 one-topping medium pizza for $7.99 or 2 one-topping medium pizzas for $6.49 each.” (1 point) Responses $12.98 $12.98 $3 $3 $15.98 $15.98 $14.48
The incentive offers two options for purchasing medium one-topping pizzas:
Option 1: Purchase 1 medium one-topping pizza for $7.99
Option 2: Purchase 2 medium one-topping pizzas for $6.49 each
To find the total price when two medium one-topping pizzas are purchased with the incentive, we need to calculate the cost for each option.
Option 1:
1 medium one-topping pizza for $7.99
Option 2:
2 medium one-topping pizzas for $6.49 each
Total cost = 2 * $6.49 = $12.98
Therefore, the correct answer is:
The total price when two medium one-topping pizzas are purchased with the incentive is $12.98.
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 find the higher resulting balance after investing $500 for a period of 10 years, we can use the formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal investment amount = $500
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested for
For simple interest at 8%, the formula is:
A = P(1 + rt)
For compound interest at 9%, let's assume that it is compounded annually, so n = 1.
Calculating the balances for each interest rate:
Simple interest at 8%:
A = $500(1 + 0.08*10) = $1,400
Compound interest at 9%:
A = $500(1 + 0.09/1)^(1*10)
A = $500(1.09)^10
A ≈ $1,956.99
Therefore, the higher resulting balance after investing $500 for a period of 10 years is approximately $1,956.99.