Find the present value of $9000 due at the end of 18 years at 11% per annum compounded quaterly????
r=11%/4=0.0275 per quarter
n=18*4 quarters=72 quarters
FV=PV*(1+r)n
PV=FV/(1+r)n
=9000/(1.0275)72
=9000/7.0517
=1276.29
To find the present value of $9000 due at the end of 18 years at 11% per annum compounded quarterly, you can use the formula for compound interest:
Present Value = Future Value / (1 + r/n)^(nt)
Where:
Future Value = $9000
r = annual interest rate (in decimal form) = 11% = 0.11
n = number of compounding periods per year = 4 (since it is compounded quarterly)
t = number of years = 18
Plug in the values in the formula:
Present Value = $9000 / (1 + 0.11/4)^(4*18)
Now, let's simplify the expression within the parentheses:
Present Value = $9000 / (1 + 0.0275)^(72)
Next, calculate the exponent:
Present Value = $9000 / (1.0275)^(72)
Using a calculator or spreadsheet, compute (1.0275)^72:
Present Value = $9000 / 2.602932
Finally, divide $9000 by 2.602932 to find the present value:
Present Value ≈ $3463.85
Therefore, the present value of $9000 due at the end of 18 years at 11% per annum compounded quarterly is approximately $3463.85.