Question

Question 24 (1 point) What is the cash value of $5000 if it is discounted for 5 years at 10% compounded yearly? OA) $3143.28 OB) $3000.61 OC) $3228.43 OD) $3100.61 O E) $3104.61

Answer 1

In calculating the cash value of a future sum, we are interested in knowing what an amount of money receivable n years hence is worth today at a given rate of interest r. The process of calculation is as below:

Cash Value= FV / (1+r)ⁿ {read as FV divided by (one plus discount rate in decimals)ⁿ}

​where:

FV = Future Value which is $5000 in this case

r = Rate of discount which is 10% in this case

n = Number of years or compounding periods which is 5 in this case​

Hence, the cash value of $5000 discounted @ 10% per annum compounded annualy for 5 years can be calculated as below:

5000 / (1+0.1)⁵

= 5000 / (1.1)⁵

Now, using a simple calculator, we can solve the value of (1.1)⁵ by simply dividing 1 by 1,1 and pressing the multiply button. This will give cash value of future Re. 1 for the first year. Then press the = button 4 times (5 minus one for which the result is alraedy displayed on the calculator screen). The resultant figure will be the cash value of future Re. 1 for the fifth year. Then multiply the resulting figure with the desired amount to get its cash value.

Very Important Caution: Do not press any other button on the calculator while making this calculation.

Solving (1.1)⁵ by the method explained above we get a figure of 0.620921.

Multiplying 0.620921 with $ 5000 we get its cash value  discounted @ 10% per annum compounded annualy for 5 years as $5000 * 0.620921 = $ 3104.61

The correct answer therefore is E