A heat exchanger has been designed for use in a chemical process.

A standard type of heat exchanger with a negligible scrap value costs \(\$ 4,000\) and will have a useful life of \(6 \mathrm{yr}\). Another proposed heat exchanger of equivalent design capacity costs \(\$ 6,800\) but will have a useful life of \(10 \mathrm{yr}\) and a scrap value of \(\$ 800\). Assuming an effective compound interest rate of \(8 \% / \mathrm{yr}\), determine which heat exchanger is cheaper by comparing the capitalized costs.