If 8000 dollars is invested in a bank account at an interest rate of 10 per cent per year, find the amount in the bank after 15 years if interests is compounded monthly
To find the amount in the bank after 15 years with monthly compounding interest, we'll use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the total amount including the principal
P = the principal amount (the initial investment)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
In this case:
P = $8000
r = 10% = 0.10 (as a decimal)
n = 12 (since interest is compounded monthly)
t = 15 years
Now we can plug in these values into the formula:
A = 8000(1 + 0.10/12)^(12*15)
A = 8000(1 + 0.008333)^180
A = 8000(1.008333)^180
A ≈ 8000(2.769)
A ≈ $22,152
So, the amount in the bank after 15 years, with monthly compounded interest, would be approximately $22,152.