Amount wanted after 3 years is 300,000 and 500,000 after 5 years. Find present value of p when 12peecent interest is compounded bimonthly.

1. P = Po*(1+r)n.

Po = $300.000.

r = 0.12/12 * 2mo. = 0.02 = Bi-monthly % rate expressed as a decimal.

n = 6comp./yr. * 3yrs. = 18 Compounding periods.

300,000 = Po(1+0.02)^18.
Po = 300,000/1.02^18 = $210,048.

2. Same procedure as #1 except for 5 yrs. and $500,000.

To find the present value (P) when the amount wanted after 3 years and 5 years is known, we need to use the compound interest formula:

A = P(1 + r/n)^(nt)

Where:
A = Amount wanted after the given time period
P = Present value (the initial investment)
r = Annual interest rate (expressed as a decimal)
n = Number of times interest is compounded per year
t = Number of years

In this case, we have the following information:
Amount wanted after 3 years (A1) = $300,000
Amount wanted after 5 years (A2) = $500,000
Interest rate (r) = 12% = 0.12 (expressed as a decimal)
Number of times compounded per year (n) = 12 (bimonthly: there are 12 months in a year)
Number of years (t1 = 3 years, t2 = 5 years)

Let's calculate the present value (P) step by step:

Step 1: Calculate P for the first time period (3 years):
A1 = P(1 + r/n)^(nt1)
300,000 = P(1 + 0.12/12)^(12*3)
300,000 = P(1.01)^(36)
300,000/1.01^36 = P
P ≈ $232,887.76

Step 2: Calculate P for the second time period (5 years):
A2 = P(1 + r/n)^(nt2)
500,000 = P(1 + 0.12/12)^(12*5)
500,000 = P(1.01)^(60)
500,000/1.01^60 = P
P ≈ $361,308.92

Therefore, the present value (P) when the desired amounts are $300,000 after 3 years and $500,000 after 5 years, with a 12% interest rate compounded bimonthly, is approximately $232,887.76 and $361,308.92, respectively.

To find the present value, we need to use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = Final amount
P = Present value (what we want to find)
r = Annual interest rate (as a decimal)
n = Number of times the interest is compounded per year
t = Number of years

From the given information, we know that:
A₁ = $300,000 after 3 years
A₂ = $500,000 after 5 years
r = 12% or 0.12 (as a decimal)
n = 12 (compounded bimonthly)

First, let's calculate the present value after 3 years. Using the formula, we have:

A₁ = P(1 + r/n)^(nt)
$300,000 = P(1 + 0.12/12)^(12*3)

Now, let's solve for P:

P = $300,000 / (1 + 0.12/12)^(12*3)

Using a calculator, calculate the expression inside the parentheses:
(1 + 0.12/12)^(12*3) ≈ 1.43743

P = $300,000 / 1.43743
P ≈ $208,440.34

Therefore, the present value (P) is approximately $208,440.34 when compounded bimonthly at a 12% interest rate.