Question

Given that i=6%,s=4% and n=5 years, calculate (a) Future value of $2,500 per year with formula of FV being (b) Present value of $2,500 per year (in arrears) for 5 years with I=6% (c) Annual sinking fund to be set aside so that at the end of the 5 years, the total sinking fund accumulated for the 5 years is to reach $200,000.

Answer 1

(a) Future value: $14,092.71, (b) Present value: $10,530.83, (c) Annual sinking fund: $35,436.53.

Step-by-step explanation:

(a) Future value of $2,500 per year for 5 years with an interest rate of 6%:

FV = 2500 x (1 + 0.06)^5 - 1} / {0.06}

FV ≈ 2500 x (1.06)^5 - 1} / {0.06}

FV ≈ 2500 x (1.338225 - 1} / {0.06}

FV ≈ 2500 x {0.338225} / {0.06}

FV ≈ 2500 x 5.63708333

FV ≈ 14,092.71

So, the future value is approximately $14,092.71.

(b) Present value of $2,500 per year (in arrears) for 5 years with an interest rate of 6%:

PV = 2500 x {1 - (1 + 0.06)^{-5}} / {0.06}

PV ≈ 2500 x {1 - (1.06)^{-5}} / {0.06}

PV ≈ 2500 x {1 - 0.74726} / {0.06}

PV ≈ 2500 x {0.25274} / {0.06}

PV ≈ 2500 x 4.21233333

PV ≈ 10,530.83

So, the present value is approximately $10,530.83.

(c) Annual sinking fund to reach $200,000 in 5 years:

SF = 200000 / (1 + 0.06)^5 - 1} / {0.06}

SF ≈ 200000 / (1.06)^5 - 1} / {0.06}

SF ≈ 200000 / 1.338225 - 1 / {0.06}

SF ≈ 200000 /{0.338225} / {0.06}

SF ≈ 200000 / 5.63708333

SF ≈ 35,436.53

So, the annual sinking fund amount is approximately $35,436.53.