**Question**: A small airline executive charter company needs to borrow $160,000 to purchase a prototype synthetic vision system for one of its business jets. The SVS is intended to improve the pilots’ situational awareness when visibility is impaired. The local (and only) banker makes this statement: “We can loan you $160,000 at a very favorable rate of 12% per year for a five-year loan. However, to secure this loan, you must agree to establish a checking account (with no interest) in which the minimum average balance is $32,000. In addition, your interest payments are due at the end of each year, and the principal will be repaid in a lump-sum amount at the end of year five.” What is the true effective annual interest rate being charged?

**Answer**. The cash-flow diagram from the banker’s viewpoint appears below. When solving for an unknown interest rate, it is good practice to draw a cashflow diagram prior to writing an equivalence relationship. Notice that P_{0} = $160,000 − $32,000 = $128,000. Because the bank is requiring the company to open an account worth $32,000, the bank is only $128,000 out of pocket. This same principal applies to F5 in that the company only needs to repay $128,000 since the $32,000 on deposit can be used to repay the original principal.

The interest rate (IRR) that establishes equivalence between positive and negative cash flows can now easily be computed:

*P*_{0} = *F*_{5}(*P*/*F*, *i* ′ %, 5) + *A*(*P*/*A*,* i* ′ %, 5),

$128,000 = $128,000(*P*/*F*,* i* ′ %, 5) + $19,200(*P*/*A*, *i* ′ %, 5).

If we try *i* ′ = 15%, we discover that $128,000 = $128,000.

Therefore, the true effective interest rate is 15% per year.