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 quarterly
To find the amount in the bank after 15 years with quarterly compounding, we use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount in the bank account
P = the principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of compounding periods per year
t = number of years
In this case:
P = $8000
r = 10% = 0.10
n = 4 (quarterly compounding)
t = 15 years
Plugging in these values into the formula, we have:
A = 8000(1 + 0.10/4)^(4*15)
A = 8000(1 + 0.025)^(60)
A = 8000(1.025)^(60)
Calculating this, we get:
A ≈ $31533.28
So, the amount in the bank after 15 years with quarterly compounding would be approximately $31,533.28.