If 3000 dollars is invested in a bank account at an interest rate of 9 per cent per year, find the amount in the bank after 5 years if interest is compounded annually
To find the amount in the bank after 5 years with compound interest, we can use 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 (initial deposit)
r = annual interest rate (as a decimal)
n = number of times that interest is compounded per year
t = number of years
Given that:
P = $3000
r = 9% = 0.09 (as a decimal)
n = 1 (compounded annually)
t = 5 years
Using this information, we can substitute the values into the formula:
A = 3000(1 + 0.09/1)^(1*5)
Simplifying the equation:
A = 3000(1.09)^5
Calculating:
A ≈ 3000 * 1.53862
A ≈ $4615.85
Therefore, the amount in the bank after 5 years, with compound interest, is approximately $4615.85.
To find the amount in the bank after 5 years with annual compounding interest, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial investment)
r = the annual interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the number of years
In this case, the principal amount (P) is $3000, the annual interest rate (r) is 9% or 0.09 (as a decimal), the number of times interest is compounded per year (n) is 1 (since it's compounded annually), and the number of years (t) is 5.
Plugging these values into the formula:
A = 3000(1 + 0.09/1)^(1*5)
A = 3000(1 + 0.09)^5
A = 3000(1.09)^5
A ≈ 4155.99
So, the amount in the bank after 5 years with annual compounding interest would be approximately $4155.99