Question

How much should be set aside today to pay for the perpetual maintenance of a bridge, in the amount of $2,000,000 every five years - indefinitely - if interest is assumed to be 4.2% annually?

Answer 1

As per the question the perpetual Maintenance cost of the bridge in every 5 year = $2,000,000

Life of the bridge (N) = ∞ (infinite)

Rate of interest (i) = 4.2% = 0.042

First we need to convert the recurring maintenance cost into EUAW for the first 5 year

Then A = $2,000,000(A/F,4.2%,5)

A = $2,000,000[i/{(1+i)N-1}]

A = $2,000,000[0.042/{(1+0.042)5-1}]

A = $2,000,000[0.042/{(1.042)5-1}]

A = $2,000,000[0.18389067818] = $367,781.3564

Now the EUAW is used for calculation of perpetual maintenance cost of bridge

The perpetual maintenance cost of the bridge = $367,781.3564(P/A,4.2%,∞)= $367,781.3564/0.042 =$8,756,698.9619    or   Approx $8,756,698.96

The amount to be saved today for the perpetual maintenance cost of the bridge is = $8,756,698.96