How much money will be needed to supplement the sinking fund?

Question

The following scheduled of funds is available to form a sinking fund.\begin{array}{|c|c|c|c|} \hline Currentyear(n)& $5000 \\ \hline n+1& $4000 \\ \hline n+2& $3000 \\ \hline n+3& $2000\\ \hline \end{array} At the end of the 4th year , equipment costing P25,000 will have to be purchased as replacement for the old equipment. Money is valued at 20% by the company. At the time of purchase, how much money will be needed to supplement the sinking fund?

Answer 1

Use the future value of the cash flows at the end of the fourth year.

We use the compound interest formula applied for each year's funds and total them up.

$$A = P\bigg(1 + {r \over n}\bigg)^{nt}$$

$\$5000$ at the end of 4 years becomes: $\$5000 \bigg(1 + {0.20 \over 1}\bigg)^{4 \times 1} = \$10368$

$\$4000$ at the end of 3 years becomes: $\$4000 \bigg(1 + {0.20 \over 1}\bigg)^{3 \times 1} = \$6912$

$\$3000$ at the end of 2 years becomes: $\$3000 \bigg(1 + {0.20 \over 1}\bigg)^{2 \times 1} = \$4320$

$\$2000$ at the end of 1 years becomes: $\$2000 \bigg(1 + {0.20 \over 1}\bigg)^{1 \times 1} = \$2400$

This gives a total fund value of $\$24,000$ at the end of 4th year. If you need to purchase equipment worth $\$25,000$, you will be short of $\$1,000$ and you need to replenish at least $\$1,000$