Question

Calculate the present worth of 11 uniform payments of $9,000 that begin 1 year from now at an interest rate of 8% per year.

The present worth is $  .

Answer 1

Interest rate = 8% per year

C₁ = C₂ =...... =C₁₁ = $9000

Presen value of cash flow C_n can be calculated using the below formula:

PV = C_n/(1+r)ⁿ

PV of C₁ = 9000/(1+8%)¹ = 8333.33

PV of C₂ = 9000/(1+8%)² = 7716.04938271605

PV of C₃ = 9000/(1+8%)³ = 7144.49016918153

PV of C₄ = 9000/(1+8%)⁴ = 6615.26867516808

PV of C₅ = 9000/(1+8%)⁵ = 6125.24877330378

PV of C₆ = 9000/(1+8%)⁶ = 5671.52664194794

PV of C₇ = 9000/(1+8%)⁷ = 5251.4135573592

PV of C₈ = 9000/(1+8%)⁸ = 4862.41996051778

PV of C₉ = 9000/(1+8%)⁹ = 4502.24070418313

PV of C₁₀ = 9000/(1+8%)¹⁰ = 4168.74139276216

PV of C₁₁ = 9000/(1+8%)¹¹ = 3859.94573403904

Present value of all 11 uniform payment is the sum of the present value of individual payments

Therefore, total present value = 64250.678324512

Answer -> $64,250.68

Period	1	2	3	4	5	6	7	8	9	10	11
Payment	9000	9000	9000	9000	9000	9000	9000	9000	9000	9000	9000
Present Value	8333.333	7716.049	7144.49	6615.269	6125.249	5671.527	5251.414	4862.42	4502.241	4168.741	3859.946