Jungle Jim owes three debts:

$500 due in one year plus interest at 6% compounded semi-annually,
$2000 due in two years,
$1000 due in three years plus interest at 5% compounded monthly.

He wishes to discharge these debts by paying $500 now and two equal but unknown payments in one and two years respectively. Find the size of the equal payments if money is, at present, worth 12% compounded quarterly. Use a focal date of two years.

kenny has £3200 in a saving account.after a year, the bank pays him interest increasing his balance to £3360. what percentage rate was applied to the account?

To find the size of the equal payments that Jungle Jim needs to make, we can use the concept of present value. Present value is the current worth of a future sum of money, considering the time value of money and the interest rate.

Let's break down the problem step by step:

Step 1: Calculate the present value of each debt using the given interest rates:

For the first debt of $500 due in one year, compounded semi-annually at 6% interest, we can use the formula for present value:

PV = FV / (1 + r/n)^(n*t)

Where:
PV = Present value
FV = Future value
r = Annual interest rate
n = Number of compounding periods per year
t = Number of years

Using the formula:

PV1 = $500 / (1 + 0.06/2)^(2*1)
= $500 / (1 + 0.03)^2
= $500 / (1.03)^2
≈ $457.92

For the second debt of $2000 due in two years, we can calculate the present value as:

PV2 = $2000 / (1 + 0.12/4)^(4*2)
= $2000 / (1 + 0.03)^8
= $2000 / (1.03)^8
≈ $1421.34

For the third debt of $1000 due in three years, compounded monthly at 5% interest, we can calculate the present value as:

PV3 = $1000 / (1 + 0.05/12)^(12*3)
= $1000 / (1 + 0.00417)^36
≈ $827.02

Step 2: Determine the total present value of all debts:

Total PV = PV1 + PV2 + PV3
= $457.92 + $1421.34 + $827.02
≈ $2706.28

Step 3: Find the size of the equal payments:

To discharge the debts, Jungle Jim plans to make two equal payments at one year and two years from now. Since the focal date is two years, we can calculate the equal payments using the formula for present value:

Total PV = Payment1 / (1 + r/4) + Payment2 / (1 + r/4)^2

Substituting the values:

$2706.28 = Payment1 / (1 + 0.12/4) + Payment2 / (1 + 0.12/4)^2

Simplifying the equation:

$2706.28 = Payment1 / 1.03 + Payment2 / 1.03^2

Now, let's solve for the equal payments, Payment1 and Payment2, using algebraic techniques:

$2706.28 = Payment1 / 1.03 + Payment2 / 1.0609

Since the equal payments are unknown, let's represent them as x:

$2706.28 = x / 1.03 + x / 1.0609

To eliminate the denominators, we can multiply the equation by (1.03 * 1.0609):

$2706.28 * (1.03 * 1.0609) = x * 1.0609 + x * 1.03

$2706.28 * 1.0931827 = 2.0949x

Dividing both sides by 2.0949:

$2706.28 * 1.0931827 / 2.0949 = x

x ≈ $1415.53

So, Jungle Jim needs to make equal payments of approximately $1415.53 at one year and two years from now to discharge his debts.

Note: The numbers provided in the calculation are rounded for ease of understanding.