An investment pays you $100 at the end of each of the next 3 years. The investment will then pay you $200 at the end of Year 4, $300 at the end of Year 5, and $500 at the end of Year 6. If the interest rate earned on the investment is 8 percent, what is its present value? What is its future value?

Question

Business

Angus

21 August, 04:54

An investment pays you $100 at the end of each of the next 3 years. The investment will then pay you $200 at the end of Year 4, $300 at the end of Year 5, and $500 at the end of Year 6. If the interest rate earned on the investment is 8 percent, what is its present value? What is its future value?

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Answers (1)

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Emerson Molina · Answer 1

Present value is $923.90 and future value is $1,466.24

Explanation:

Given:

$100 is received in the next three years. It's an annuity so refer present value of annuity table. Present value annuity factor for 3 years, 8% is 2.5771. So present value of this will be $257.71 (2.5771 * 100). Similarly calculation for inflows from the investment are as follows:

$200 at 8% in the 4th year, present value factor of lumpsum amount is 0.7350 which is $147 (0.735 * 200)

$300 at 8% in the 5th year, present value factor of lumpsum amount is 0.6806 which is $204.18 (0.6806 * 300)

$500 at 8% in the 6th year, present value factor of lumpsum amount is 0.6302 which is $315.10 (0.6302 * 500)

Total present value of investment is $923.90 (257.71 + 147 + 204.18 + 315.10)

Present value of inflows are calculated. Calculate future value of these amounts.

future value factor @8%, 6 years is 1.5869.

Future value of first inflow is $408.96 (257.71 * 1.5869)

Future value of second inflow is $233.27 (147 * 1.5869)

Future value of third inflow is $324.01 (204.18 * 1.5869)

Fourth Inflow in the sixth year is $500

Total present value of investment is $1,466.24 (408.96 + 233.27 + 324.01 + 500)