A freight-hauling firm estimates that it will need a new forklift in six years. The estimated cost of the vehicle is $40,000. The company sets up a sinking fund that pays 8% compounded semiannually, into which it will make semiannual payments to achieve the goal. Calculate the size of the payments. **Show work**

A)

$1323.71

B)

$2107.80

C)

$1023.47

D)

$2662.09

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- The above answer is incorrect. Below is given the correct answer.
- v_pandey
- May 07, 2018 at 4:21am

- Future value of ordinary annuity: The future value of an ordinary annuity is defined as measurement of the amount obtained in some future time when the specified rate of return is given. If the rate of return is high, then the value annuity will also be higher because the annuity will grow at the required rate of return. When payments are made at the end it is known as ordinary annuity. By extracting the information: Future value = $40000 Time to maturity = 6 Interest rate = 8% Compounding period (m) = 2 Calculate the instalment amount:
- v_pandey
- May 07, 2018 at 4:22am

- To calculate the Payment the formula is as follows: Payment = Future value / [((1 + r/m) nxm - 1) / (r/m)]
- v_pandey
- May 07, 2018 at 4:22am

- By substituting the values:
- v_pandey
- May 07, 2018 at 4:22am

- Payment = $40000 / [((1 + 0.08/2) ^(6x2) - 1) / (0.08/2)] = 2662.09
- v_pandey
- May 07, 2018 at 4:24am

- Thus the payment is 2662.09
- v_pandey
- May 07, 2018 at 4:24am

- The correct option is (D)
- v_pandey
- May 07, 2018 at 4:24am