Jesper Parnevik borrowed $70,000 on March 1, 2012. This amount plus accrued interest at 12% compounded semiannually is to be repaid March 1, 2022. To retire this debt, Alex plans to contribute to a debt retirement fund five equal amounts starting on March 1, 2017, and for the next 4 years. The fund is expected to earn 10% per annum

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To find the equal amounts that Alex needs to contribute to the debt retirement fund, we can divide the total debt by the present value factor of an annuity.

Step 1: Calculate the total debt including accrued interest:
The principal borrowed is $70,000. We need to calculate the interest accrued over the 10-year period using a 12% interest rate compounded semiannually.
The formula to calculate the future value (FV) of an amount with compound interest is:
FV = PV * (1 + r/n)^(nt)

Where:
FV = Future Value
PV = Present Value (Principal)
r = Annual Interest Rate
n = Number of times interest is compounded per year
t = Number of years

In this case, r = 12% or 0.12, n = 2 (since interest is compounded semiannually), and t = 10 years.

FV = $70,000 * (1 + 0.12/2)^(2*10)
FV = $70,000 * (1.06)^20
FV ≈ $191,031.52

So, the total debt including accrued interest is approximately $191,031.52.

Step 2: Calculate the present value factor of an annuity:
The present value factor of an annuity is used to determine the equal periodic payment required to pay off a debt over a specific period.
The formula to calculate the present value (PV) of an amount with an annuity is:
PV = Pmt * [(1 - (1 + r/n)^(-nt)) / (r/n)]

Where:
PV = Present Value (Principal)
Pmt = Equal periodic payment
r = Annual Interest Rate
n = Number of times interest is compounded per year
t = Number of years

In this case, r = 10% or 0.10, n = 1 (since the fund earns interest annually), and t = 4 years.

PV = Pmt * [(1 - (1 + 0.10/1)^(-1*4)) / (0.10/1)]
PV = Pmt * [(1 - (1.1)^(-4)) / 0.10]

Step 3: Solve for Pmt:
To find the equal periodic payment required, we'll solve the equation from step 2 for Pmt:
Pmt = PV / [(1 - (1.1)^(-4)) / 0.10]

Using a calculator, we can plug in the values:
Pmt = $191,031.52 / [(1 - (1.1)^(-4)) / 0.10]
Pmt ≈ $58,772.70

Therefore, Alex needs to contribute approximately $58,772.70 into the debt retirement fund each year for the next 4 years to retire the debt.