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## Q. 10.5

Calculate the payback period for a PV system with $6000 cost after tax rebates, an output of 2000 kWh/year,$0.13/kWh cost of electricity, and$MARR^{2} = 2$%.

## Verified Solution

From above, the ratio P/A is 23.1 to the nearest tenth. Recalling P/A as a function of i and N:

$P / A=\frac{\left[(1+i)^{N}-1\right]}{i(1+i)^{N}}=\frac{\left[(1.02)^{N}-1\right]}{0.02(1.02)^{N}}=23.1$

Rearranging terms to solve for N gives

(1.02)$^{N}$ = 1.859

Thus N = 31.3, or 31.3 years is the length of the payback period. Even with a relatively low MARR of 2% (i.e., the owner is willing to forego earning return on investment at market rates), the payback period has increased by over 8 years.

Note that the long payback for the system, whether simple payback or with MARR = 2%, is a function in part of the relatively low insolation in the region. As an illustration, in a sunnier region which averaged 125 kWh/kW/month downstream from the inverter, the simple payback is reduced to 14 years, all other things held constant.