1. Ashlyn took out a loan for $700 to buy a new Tv. The bank to going to charge her 3% compound interest. What amount will Ashlyn owe the bank after 3 years
2. Determine the value of a $100 investment earning 10% compound interest over 2 years.
2.
value=100(1.10)^2
1. 700(1.03)^3
Thank you
To calculate the amount that Ashlyn will owe the bank after 3 years with compound interest, we need to use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount of the loan including interest
P = the principal amount (the initial loan amount)
r = the annual interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the number of years
1. For Ashlyn's situation, the principal amount (P) is $700, the annual interest rate (r) is 3% (or 0.03 as a decimal), and she will be charged compound interest once a year (n = 1). The time period (t) is 3 years.
Plug in these values into the compound interest formula:
A = 700(1 + 0.03/1)^(1*3)
A = 700(1 + 0.03)^3
A = 700(1.03)^3
A ≈ 742.02
Therefore, Ashlyn will owe the bank approximately $742.02 after 3 years.
2. Similarly, for the second question, we have a $100 investment earning 10% compound interest over 2 years. Using the same formula:
A = P(1 + r/n)^(nt)
P = $100, r = 10% (or 0.10 as a decimal), n = 1 (compounded once a year), and t = 2 years.
Plug in these values:
A = 100(1 + 0.10/1)^(1*2)
A = 100(1 + 0.10)^2
A = 100(1.10)^2
A = 100(1.21)
A = $121
Therefore, the value of the $100 investment after 2 years with a 10% compound interest is $121.