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You are working for an equipment leasing company, and your boss has asked you to calculate the half-yearly lease payments for new equipment for a client. The cost of the equipment is $68,000 and the lease term is 8 years. The interest rate is 11.2% p.a. compounding semi-annually. The lease requires lease payments that are the same every half-year, except for the final payment which is a residual/lump sum payment of $9,000. Assuming the lump sum payment is made in the final half-year period (16), calculate the half-yearly lease amount for the other 15 periods. Type your answer as a positive number into the box in dollar and cents (i.e. 2 decimal places and no negative (-) symbol).(Ignore taxes and depreciation. Assume lease payments occur at the end of each period.)

Question

You are working for an equipment leasing company, and your boss has asked you to calculate the half-yearly lease payments for new equipment for a client. The cost of the equipment is 68,000andtheleasetermis8years.Theinterestrateis11.268,000 and the lease term is 8 years. The interest rate is 11.2% p.a. compounding semi-annually. The lease requires lease payments that are the same every half-year, except for the final payment which is a residual/lump sum payment of 9,000. Assuming the lump sum payment is made in the final half-year period (16), calculate the half-yearly lease amount for the other 15 periods. Type your answer as a positive number into the box in dollar and cents (i.e. 2 decimal places and no negative (-) symbol).(Ignore taxes and depreciation. Assume lease payments occur at the end of each period.)

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Solution

To calculate the half-yearly lease amount for the other 15 periods, we need to use the formula for the present value of an annuity. The present value of an annuity is calculated as:

PV = Pmt * [(1 - (1 + r)^-n) / r]

Where:

  • PV is the present value of the annuity
  • Pmt is the periodic payment
  • r is the periodic interest rate
  • n is the number of periods

In this case, we know the present value of the annuity (the cost of the equipment minus the residual value), the periodic interest rate (the annual interest rate divided by 2), and the number of periods (the lease term in years times 2). We can rearrange the formula to solve for Pmt:

Pmt = PV / [(1 - (1 + r)^-n) / r]

Substituting the given values:

PV = 68,00068,000 - 9,000 = $59,000 r = 11.2% / 2 = 5.6% = 0.056 n = 8 * 2 = 16

Pmt = $59,000 / [(1 - (1 + 0.056)^-16) / 0.056]

Calculating the right side of the equation:

Pmt = $59,000 / [(1 - 0.056)^-16 / 0.056]

Pmt = $59,000 / [7.96]

Pmt = $7,412.06

Therefore, the half-yearly lease amount for the other 15 periods is $7,412.06.

This problem has been solved

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