calculate the present value AND the compound interest for this investment, round to the nearest cent...$20.000 with a nominal rate of 14% for 30 months ( semiannually)
P = Po(1+r)^n
r = (14%/2)/100% = 0.07 = Semi-annual %
rate expressed as a decimal.
n = 2comp./yr. * 2.5yrs. = 5 Compounding
periods.
P = Po(1+0.07)^5 = $20,000
Po = 20000/1.07^5 = $14,259.72
I=P-Po = 20,000 - 14,259.72 = $5,740.28
To calculate the present value and compound interest for an investment, we need to use the formulas for present value and compound interest.
First, let's calculate the present value (PV) using the formula:
PV = FV / (1 + r/n)^(n*t)
Where:
PV = Present Value
FV = Future Value (initial investment amount)
r = Nominal interest rate (as a decimal)
n = Number of compounding periods per year
t = Number of years
Given:
FV = $20,000
r = 14% (or 0.14 as a decimal)
n = 2 (semiannual compounding)
t = 30 months (or 2.5 years)
Now, let's plug in these values into the formula:
PV = $20,000 / (1 + 0.14/2)^(2*2.5)
Simplifying the equation further:
PV = $20,000 / (1 + 0.07)^5
PV = $20,000 / (1.07)^5
PV = $20,000 / 1.402552
Calculating the value:
PV ≈ $14,254.15 (rounded to the nearest cent)
Now let's calculate the compound interest using the formula:
Compound Interest = PV - FV
Compound Interest = $14,254.15 - $20,000
Compound Interest ≈ -$5,745.85 (rounded to the nearest cent) - This means the investment will result in a loss.
Therefore, the present value of the investment is approximately $14,254.15, and the compound interest is approximately -$5,745.85.