Question

What is the equal payment series for 10 years that is equivalent to a payment series of P12,000 at the end of the first year, decreasing by P1000 each year over 10 years. Interest is 8%, compounded annually.

Answer 1

The given payment series is as follows -

P12,000 at the end of the first year.

Amount decreases every year by P1000. This is the aritmentic gradient (G) of the given cash flow series.

Interest rate = 8%

Time period = 10 years

Calculate the present worth of cash flow series -

PW = Amount in first year(P/A, i, n) - annual decrease(P/G, i, n)

PW = P12,000(P/A, 8%, 10) - P1000(P/G, 8%, 10)

PW = [P12,000 * 6.71008] - [P1000 * 25.97683]

PW = P80,520.96 - P25,976.83

PW = P54,544.13

The present worth of the given cash flow series is P54,544.13

Now, we have to calculate the annual worth from this present worth to get the equal payment series.

AW = Present worth(A/P, i, n)

AW = P54,544.13(A/P, 8%, 10)

AW = P54,544.13 * 0.14902

AW = P8,128.17

Thus,

The equal payment series is P8,128.17.