# Interest rate (12_interest_rate)¶

## Description¶

The interest rate module describes interest rates and the annuity-due used in the model. The data of interest rates is used as interest rates, a risk-accounting factor associated with long-term investment (Wang et al1 2015). These two factors are required for inter-temporal calculations in the model such as shifting investment from one time step to another or distribution one-time investments over several time steps. An annuity-due is an annuity whose payments are made at the beginning of each period (Jordan et al22000). The annuity due is then used in the modules (13_tc, 39_landconversion, 41_area_equipped_for_irrigation, and 57_maccs) to compute the present value of annual costs.

## Interfaces¶

### Input¶

Name Description Unit A B
$sm\_invest\_horizon$ investment horizon years x x

The last columns of the table indicate the usage in the different realizations (numbered with capital letters)

### Output¶

Name Description Unit
$pm\_interest(i)$ interest rate in each region -
$pm\_annuity\_due(i)$ Annuity-due annual cash flows over n years in each region -

### Interface plot¶ Figure 0: Information exchange among modules

## Realizations¶

### (A) glo (default)¶

The glo realization is the default setting, in which the interest rate is the interest rate of 7% applied globally (Florian et al3 2014). Therefore the annuity-due is identical for each region.

\begin{equation}
\begin{split}
p12\_annuity\_due = \frac{1-(1+s12\_interest)^{-sm\_invest\_horizon}}{\frac{s12\_interest}{1+s12\_interest}} \\
pm\_interest(i) = s12\_interest \\
pm\_annuity\_due(i) = p12\_annuity\_due
\end{split}
\end{equation}

### (B) reg¶

In the reg realization, the interest rates can be regionally specific. Therefore the annuity-due can also be regionally specific.

\begin{equation}
\begin{split}
p12\_annuity\_due(i) = \frac{1-(1+f12\_interest(i))^{-sm\_invest\_horizon}}{\frac{f12\_interest(i)}{1+f12\_interest(i)}} \\
pm\_interest(i) = f12\_interest(i) \\
pm\_annuity\_due(i) = p12\_annuity\_due(i)
\end{split}
\end{equation}

The country level data of real interest rates, from the World Development Indicators, is aggregated to regional interest rates using countries' GDP as a weight. Then the average is taken between the aggregated discount rates for each MAgPIE region between 1995 and 2005 (Figure 1). Figure 1: Regionally specified interest rates

## Defintions¶

Name Description Unit A B
$sm\_invest\_horizon$ investment horizon - x x
$s12\_interest$ global interest rate - x
$f12\_interest(i)$ interest rate in each region - x
$p12\_annuity\_due(i)$ annuity factor for each region - x
$p12\_annuity\_due$ annuity factor for each region - x

The last columns of the table indicate the usage in the different realizations (numbered with capital letters)

## Developer(s)¶

Xiaoxi Wang, Florian Humpenöder, Jan Philipp Dietrich